I'll (hopefully successful) compare distributions to cars. Every car has a combustion engine that works on the same principle, in an OS that's the kernel. A subgroup of those exposes the same connectors to the outside (aka API). Linux is a even more special subgroup of those, like an engine manufactured by one company, but used by many others, that might or might not make special adaptations, but nothing too extreme.
Around that, every car has a frame, some electrics, headlights, ... Some of those are specified by law (in the UNIX world the POSIX standard), but can be adapted for special needs. As software those are called the tool set. Most Linux distributions use the GNU line of tools, as they're completely Open Source. This lead to the term "GNU/Linux" to indicate that this distribution uses the GNU tools around the Linux kernel.
But if all cars looked the same the everyday commute would be even more boring than it is now. Same goes for distributions, which is why every one of them does some small thing a bit different. They're all compatible for the most part, but differ on what software ships by default, how certain things are configured, and how to configure some very specific parts.
The currently most used distribution probably is
Ubuntu, which is derived from
Debian GNU/Linux. Another is
Fedora, which is the base for
RHEL. One of the oldest distributions still out there is
Slackware.
And then there are even more free Unices like
FreeBSD,
OpenSolaris,
NetBSD, and
MINIX. Or crossovers like
Debian GNU/kFreeBSD.