Fedora is the offshoot of Red Hat, it was used as their testing grounds for awhile, I believe, and I think RH is focusing mainly on enterprise and servers, and I believe it is no longer free.
Disclaimer: I could be wrong on any of the above, but that's what comes to mind when I hear Red Hat, for some reason.
Not exactly...but very close
Redhat is an Enterprise level linux, which means if you want to run it you pay for it. Fedora, is the Open Source project that uses Redhat's source, but has no official affiliation with Redhat itself. Redhat tosses the Open source community a bit of cash and the source and they develop an open source version and if Redhat likes anything they see, they may or may not adopt it into their enterprise level linux.
Same thing with SuSe and OpenSuSe.
The idea is you get your source code tested for free, give open source communities their source code, and if someone were to test out the free one and like it they are more inclined to buy the enterprise one. Lets face it, you aren't going to run your business off of open source linux, you are going to use Enterprise Level Linux if you are serious about it.
There are some exceptions of course. Debian is completely open source and free, and does have some enterprise like functions, as well as some Unixes as well.
What it all really comes down to though with Linux/Unix, is a few things:
1) Compatibility (typically not an issue)
2) Package Managers (everyone has something different)
3) Minor differences (which can be major in some aspects), mostly $PATH, or authentication (like some use /etc/sudoers so there is no need for a root account), how they mount things, etc