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Is Java Mission Control included with a JDK?

Are JMC binaries included in open JDK ? We have openjdk-1.8.0.252 in our Linux platform , but we do not have JMC ?
Can we install JMC as separate application that runs on JVM already installed ? Can we use JMC in production environments ?
If yes, please let me know the path to install JMC for open JDK

About Mission Control
Java Mission Control was previously a proprietary commercial offering from Oracle. Oracle then open-sourced it as a subproject on the OpenJDK project. Now available free-of-cost.
See that subproject page, Mission Control, and this wiki page. Notice the “Java” trademarked word has been dropped from the name.
As of 2021-07, the current version of the Mission Control project is 8.
Flight Recorder
Similarly Oracle’s Flight Recorder product, is now open-sourced within the OpenJDK project. See JEP 328: Flight Recorder. Flight Recorder is currently being bundled with the JDK in my experience, while Mission Control is a separate download.
Java 11
In Java 11, the current LTS version, you will need to download and install the binary of Mission Control.
Binary distributions available from various vendors. These include Azul Systems, BellSoft, Oracle, Red Hat/IBM, and Adoptium/AdoptOpenJDK.
Mission Control requires a JDK to run. Here is a flowchart I made to guide you in choosing a vendor for a JDK implementation.
Java 8
Be aware that Oracle changed its licensing on its product Oracle JDK. That product now requires a fee for use in production. As I recall, even before that change, Oracle required a fee for use of its Java Mission Control product in production.
Now Oracle has generously transferred the product to the OpenJDK project. Since open-sourcing under the OpenJDK project, other vendors are free to back-port Mission Control to Java 8 per the new licensing terms.
I know of at least one such vendor:
Azul Systems
See their product Zulu® Mission Control. This product is included with both their free-of-cost Zulu Community product and their commercial Zulu Enterprise product.

What is the reason to use OpenJDK?

I somehow understand the differences between Oracle JDK and Open JDK.
But I can't find reasons to use Open JDK.
Because Oracle JDK already has everything one would need and sometimes faster than Open JDK.
In which cases should someone use Open JDK?
Is it just for legality issues?
If yes, then what are issues?
That because I have been still develop all my projects using Oracle JDK

Other Answers are correct. Here is some other information as well, including vital changes as of early 2021.
Source-code versus Binaries/installers
understand the differences between Oracle JDK and Open JDK.
To sum it up: source-code versus binaries/installers.
OpenJDK is an open-source project, implementing the Java Specifications, JSRs, and JEPs that define the Java platform. This project publishes only source-code, not binaries or installers to get Java running on your computer (except for some early-access builds). Oracle is the principal participant in the OpenJDK project, alongside IBM & Red Hat, Apple, SAP, Azul Systems, Microsoft, and others.
Many companies provide distributions of OpenJDK for installation, as binaries or installers. Oracle is one such company.
Oracle actually provides two such products:
Oracle JDKA commercial product, with paid support plans. (Free-of-cost only for development & testing, not deployment. Read their terms.)
jdk.java.netA build of the OpenJDK source-code, freely available, unsupported.
Oracle has declared their intention to keep their commercial product Oracle JDK at feature-parity with OpenJDK. Oracle even went so far as to open-source and make available at no cost their formerly commercial tools Mission Control and Flight Recorder, both now a part of OpenJDK. So there is nearly no practical difference. One significant difference is that the Oracle company reserves the right to rapidly supply their paid support customer base with urgent patches not currently found in OpenJDK. Ditto for other vendors selling support.
[And for the record, Oracle offers a third implementation of Java, GraalVM, which is a very specialized product.]
Here is a flowchart graphic I made to help guide you in selecting a provider of a Java implementation.
And here is a list of motivations you might consider in choosing a distribution.

November 2017: At the time this question was asked, the reasons for choosing between OpenJDK and Oracle JDK include:
Availability of builds / installers for specific platforms. For example, last time I checked there were no Oracle JDK distros in ".deb" format for Debian / Ubuntu. And no OpenJDK builds for Windows.
Oracle JDK has some commercial features that can be enabled by people who have paid. They are not present on OpenJDK.
Oracle JDK has an annoying click-through license. This is a pain if you are trying to automate deployment; e.g. to cloud VMs. By contrast, OpenJDK on Linux (at least) can be installed and updated using the platform's package manager.
There may be issues if you wanted commercial support for OpenJDK.
There were no substantive license differences between Oracle JDK and OpenJDK if you just plan to use the software. (There are some constraints on binary redistribution for Oracle JDK, but they are about shipping non-standard or stripped-down versions of the Java platform.)
In the future, some of these differences will go away, according to this blog page:
Faster and Easier Use and Redistribution of Java SE
Update in December 2018:
As of January 2019, Oracle JDK Java 8 will be EOL for commercial uses. (But free support will continue until January 2020 for personal use.)
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Java 9 and Java 10 are EOL.
Commercial uses of Oracle JDK Java 11 and later require a support contract or a subscription from Oracle. OpenJDK Java builds do not have this requirement.
Oracle do not provide support for OpenJDK Java builds, but support is available from 3rd parties. Third parties will also port Oracle security fixes to OpenJDK builds.
Further reading:
Java Is Still Free
OpenJDK Life Cycle and Support Policy (RedHat)
The future of Java and OpenJDK updates without Oracle support
What has changed in Java Release and Update Availability? (Azul Systems)
AdoptOpenJDK Support
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EOL stands for end-of-life.
An end-of-life (EOL) product is a product that does not receive continuing support, either because existing marketing, support and other processes are terminated, or it is at the end of its useful life.

OpenJDK comes tightly integrated with the distribution update process. For example, on Fedora, this means that you simply can run
dnf update
without activating third-party repositories, and you will get the latest OpenJDK version with all relevant fixes.
OpenJDK is tested by the distribution vendor on this particular distribution. Oracle has different reference platforms for testing of OpenJDK. In the case of Fedora, software written in Java is tested with the OpenJDK version provided by the distribution, while the combination of that software with Oracle JDK receives much less testing.
Oracle also bundles their Java downloads with additional software such as browser toolbars, performance measurement and monitoring tools.

For those, who read this in 2019.
Java SE 8 is the last Java SE release targeting Desktop deployment (eg, Java Web Start and a stand-alone system JRE). Java SE 8 will be end of public updates in January 2019, after which commercial users need to either transition to other technologies, or purchase a Java SE Subscription.
So, another reason to use OpenJDK (in addition to what Stephen C said): it's free of charge for all purposes.

is there a JRE reduced version for Tomcat only?

I have a web application that uses embedded Tomcat, which I'll distribute as a desktop app. Since I don't want users to deal with the installation of JRE, I decided to bundle JRE in my installation package, however, I was wondering if there's a reduced version of JRE in order of having a smaller installation file size. For example, I removed all the CORBA related files from JRE and everything seems to be working fine, so I guess some other files could be removed without affecting Tomcat's functionality, but I really don't know which other files should I remove.
If anyone has done this before, I'd appreciate your comments.

AFAIK, there aren't any official cut-down Oracle JRE releases. Certainly not free ones, though I imagine Oracle would create one for a customer who was willing to pay (enough).
If you created and distributed a cut-down JRE based on the Oracle JRE, it would be a violation of the Java Binary license ... which expressly forbids such things. You would need to get permission from Oracle to do this. The same applies to other suppliers, so the chances of you finding a free cut-down JRE based on OpenJDK are "vanishingly small".
I'm don't know for sure the legal constraints on building a cut-down JRE starting from the OpenJDK open-source codebase. I suspect that it is legal from the copyright perspective, but that you need to understand of patent and trademark issues. (For example, a cut-down JRE would not pass Java Standard Edition TCK testing, so you would not be permitted to use trademarked terms like Java and JRE to describe it.)
You should to talk to a lawyer if you intended to build and distribute cut-down JREs to anyone else.
I understand that Azul distributes cut-down JREs as a commercial (non-free) offering. Google found this for me:
The short answer for why we do not remove contents of Zulu JDK is for compliance with Java Standard Edition TCK testing. Changing the contents of tested build after the fact is often believed to be an invalidation of TCK coverage, and we cannot ship without that copyright/patent/trademark umbrella. Secondly, Azul offers cut down JREs and Compact Profile binary builds as a commercial (non-free) offering. We still need some way to monetize Zulu (else the business is not self sustaining) so charging fees and offering only private access to the set of lean & mean production runtimes is core to our business model.

Why are there differences between openJDK and oracleJDK

I have problems with the following method:
sun.security.x509.AuthorityKeyIdentifierExtension.getEncodedKeyIdentifier()
It exists in openJDK but it does not exist in oracleJDK. I always thought that except for some special cases regarding licensing those JDKs should be the same ...
While I can work around that issue, I fear there are other incompatibilities I might not be aware of.

Classes that are not part of the standard packages and classes that are deprecated can be not part of a jdk.
In your case you can try to solve the problem using the classes of the package javax.security.cert. Searching for it on google you can find some tutorials like this one.
Just to complete the answer is true that "generally" both compiled code comes from the same source code in the open jdk and in the oracle jdk. But oracle jdk and open jdk have different licences so there are also few little differences. Generally the differences are not related to the source of common classes, but to the presence or absence of classes or entire packages. As an example see the font library.
This is not the only difference. As you noted in your code also the security packages are different, because the open jdk added also the old sun version of x509 certificate classes and the oracle jdk not. There is no guarantee on what classes are included or not if they are not part of the standard packages. So if you have problems running your code on different jdk environments use only standard packages or explicitly import libraries as you need.

That class is not part of the public Java API and is therefore not guaranteed (or even likely) to exist in every JRE implementation, nor every release of the same provider's implementation.
If it's not part of the standard APIs, then you can't count on it.
Java Standard Edition 8 - all JDKs should provide these
Java Enterprise Edition 7 - some environments and libraries will provide these
While the OpenJDK and OracleJDK implementations happen to be very similar as they share a common history, they could diverge (or converge) in any private APIs or implementation details at any time, simply because they are separately-run projects.
Instead you should be using the appropriate implementation-agnostic APIs in java.security and javax.security for dealing with certificates.

Oracle JDK was previously called SUN JDK and that was before the takeover by Oracle. Earlier, it was the official proprietary implementation of the Java language. After the takeover it was named as Oracle JDK and Oracle’s team maintains the JDK.
OpenJDK is an open source implementation of the Java Standard Edition platform with contribution from Oracle and open Java community.
Actually, Oracle JDK’s build process builds from OpenJDK source code. So there is no major technical difference between Oracle JDK and OpenJDK.
Apart from the base code, Oracle JDK includes, Oracle’s implementation of Java Plugin and Java WebStart. Also includes third party closed source and open source components like graphics rasterizer and Rhino respectively.
How Oracle JDK and OpenJDK is kept in Sync:
All of the development and bug fixes happens in OpenJDK and then they are propagated to the Oracle JDK. Security fixes happens in private forest without public code reviews unlike general fixes, then they are pushed to Oracle JDK and then to OpenJDK.
more on http://javapapers.com/java/oracle-jdk-vs-openjdk-and-java-jdk-development-process/

What are the difference between ibm jdk and oracle jdk?

I'm writing Java code that will run on an AIX server. I'd like to know the difference between IBM's JDK and Oracle's JDK, and if the JDKs have the same classes. Does the IBM JDK have all the classes present in the Oracle JDK?
Are there any IBM documents that describe the differences between the two JDKs?

The biggest difference between the Oracle and IBM java runtimes is that they have independent Java Virtual Machine (JVM) and Just In Time (JIT) compiler implementations. IBM needed to build their own JVM and JIT that could run java programs on platforms such as z/OS (mainframes), AIX and Linux on Power processors, where other Java implementations would not run. The JVM and JIT are part of the Java runtime internals and they should not change how you write your Java programs. There are no documents listing the big differences between Oracle JDK and IBM, because the goal is to make them compatible. As others have said already, they are both implementing the same standard spec and Java API. That said, there is a lot of Java documentation from IBM, available at:
http://www.ibm.com/developerworks/java/jdk/docs.html
One area that could affect you as a programmer is that the IBM JRE has its own implementations of Security providers, which might need to be configured differently. These are documented in a Security Guide - the Java 8 version is here:
http://www.ibm.com/support/knowledgecenter/SSYKE2_8.0.0/com.ibm.java.security.component.80.doc/security-component/introduction.html

I work in an environment where we use Java 1.6, deploying to Oracle (JRockit), IBM and Oracle/Sun JDKs.
The three are remarkably comapatible. Apart from the occasional difference (e.g. in JAXWS startup behaviour) we strike remarkably few problems.
There are no huge holes where one JDK is missing stuff that is in others.

I meet a big difference in the GBK encoding. The ibm jvm GBK is stand for the ibm936, but the openjdk or oracle jdk is the CP936. CP936 is the real GBK standard, as knowned the windows-936. So if you meed the strange GBK problems, you can see the IBM solutions