Fedora Core is the name of the community-supported Linux distribution descended from Red Hat Linux. Even though Red Hat no longer sells a boxed version of Red Hat Linux (instead focusing on Red Hat Enterprise products), Fedora Core is the "consumer" version of the Red Hat Linux family.
As of right now, Fedora Core 2 is in the testing phase. Notable features are:
The current Fedora Core 2 release is Test 2. Try fedora.redhat.com if you aren't afraid of testing bleeding edge software. I use it and the only thing that doesn't work for me is my stupid scanner, which isn't much of a loss at all.