Ok, here's the scoop. RedHat was produced by RedHat (the company) for many years and cost nothing to download. Then at some point they decided to make it commercial, so now RedHat is called Red Hat Enterprise Linux, it costs a few bucks and they bundle support too, it's mostly for companies. But they released the RedHat code to the community and thus Fedora Core was born, effectively the non-commercial version of the same thing. Now, FC is all about rapid development, they are probably the quickest to release new applications and stuff, with possible stability problems that could entail. A lot of people still use FC in production though, so it's not a shambles, it just has occasional bugs. I haven't used it enough to really know, I've just tried it a few times.
Finally, there's also White Box, which *is* Red Hat Enterprise Linux for free and without the support.
Out of those, FC is probably the most fun.