Neither of them are based around linux, though FreeBSD is very much like Unix (even more so than linux) ...
Anyway, a linux distro contains the linux kernel and a lot of additional software which run on it, like the shell, desktop environment, applications etc. You have many distro's, Redhat, Suse, mandrake, Debian, Gentoo, Slackware being some of the popular ones.
Well, as I have not used them all, I dunno the exact differences, but I think this is the general idea (correct me if wrong) -
The first three are pretty similiar, using RPM package management, and using a style of functioning in which all the scripts associated with the runlevel you are using are collected in one directory. Each of these are also commercial linux distros, so you have both paid and free versions.
Debian uses the .deb pakage system, maybe GNURag can tell you more.
Gentoo is a unique one which has a source code based package management. The package dependencies are automatically solved, so ideally you wont have to bother much about taking care of installations.
Slackware is what I use, it doesn't have an elabourate package system, but uses .tgz packages, which is simply a collection of files and installation scripts. It doesn't use dependencies, but you can use a system like slapt-get to update your software or install new packages keeping dependencies in mind. Another way it differs is that it uses a BSD type of initialisation, there is a single script associated with each runlevel, and not a directory. It would probably be a more unixy linux