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Both Fedora and Red Hat Enterprise Linux are open source. Fedora is a community project and serves as the base platform on which RHEL is built. Fedora is a general purpose system that gives Red Hat and the rest of its contributor community the chance to premier and provide feedback on technologies that may surface later in RHEL releases. RHEL has its own set of test phases which are separate and distinct from Fedora.
The cost of RHEL comes from the subscription, which provides assorted certifications and support for additional architectures, as well as 7 years of enterprise support. Red Hat also enhances its RHEL offerings with additional software and with certification programs.
More information on the release history and lineage is available at History.
When you purchase RHEL, you are also helping to support Fedora. Since Red Hat sponsors Fedora, what is good for Red Hat is usually good for Fedora. The major differences are:
Support and associated services: Red Hat Enterprise Linux is a commercially supported product by Red Hat and provides service level agreements that is important for enterprise customers. This support involves both product assistance (hand holding) as well as prioritization of bug fixes and feature requests, certified hardware and software among other things. Fedora is supported by a wide community of developers and users but it is not commercially supported by Red Hat. Red Hat does sponsor a large number of resources and funds to the Fedora project including engineering, marketing and other services.
Lifecyle: A new version of Red Hat Enterprise Linux is released about every 18-24 months and supported for up to 7 years. New Fedora releases are available every six months and every release gets updates for about 13 months.
Software Packages: Software in Red Hat Enterprise Linux is limited to about 2500 packages. These are the ones enterprise customers demand and are supported by Red Hat. Fedora offers a wide range of software packages and the latest release has well over 12000 binary software packages available in the repository.
Software Updates: Post release updates of software in Red Hat Enterprise Linux are usually limited to backported security and bug fixes, although enhancements are also offered usually via the major scheduled updates. Red Hat also offers extended update support for customers wishing to stick to a single point release for a longer amount of time. Red Hat also aims to provide ABI compatibility within a release, whereas this is not guaranteed by the Fedora Project. Fedora software packages and updates are close to upsream and include new features routinely.
New Releases: Subscriptions are for a specified time period and not for a particular release. So you can move to any currently supported release of Red Hat Enterprise Linux including new versions of RHEL
Red Hat has a page explaining the benefits of the subscription in more detail. It also provides an older comparison between the two options.