"Linux" is actually the kernel -- the core part of the operating system. All operating systems have a kernel. But back on topic, since Linux is released under a free license called the GPL, anybody can create their own distribution of Linux. They all use basically the same software, though the versions, configuration, and approach to managing that software will vary somewhat from distro to distro.
This may seem confusing at first, but makes sense when you consider all the potential uses for a computer. Since each distro is created with a specific set of goals in mind, some are more specialized than others. Choice is good!
On my desktops I use Debian Linux, which has been around for a very long time and is backed by a non-profit organization. Debian's strength is in its amazing flexibility and huge repository of available software. It also has a very good package manager -- the part of the operating system that handles installing/removing software -- which is second to none. It's a good distribution for those who want easy access to very new versions of Linux software. A disadvantage of this approach is the potentially overwhelming amount of options this presents to a novice user.
On my servers, I am using CentOS (Community ENTerprise Operating System). If you've ever heard of Red Hat, CentOS is merely Red Hat without being branded with corporate logos, and backed by a community rather than a corporation. It's strengths include unrivaled stability, powerful security frameworks, and very long-term support cycles. Though all of these traits are important in a server OS, the latter is especially notewothy since server operating systems are not changed often. As such, getting current security patches for older server installations is important. In terms of updates, CentOS is one of the few operating systems who's updates can be automated and totally unattended without any problems at all. The disadvantage is that the software present has been tested long enough that it is often much older than that found in other distros. So while this is very nice for a server (where change can be bad), stale software is not much fun on the desktop (where change can be fun).
For my firewall, IPCop is my distro of choice. It's lightweight, simple, powerful, and can be administrated through an easy and secure web interface. IPCop is a very specialized distro, so it does not contain any desktop software, or any other software which is not necessary for it to be a good firewall. Until the last time I had a power outage, my IPCop had been up for well over 100 days without a reboot.
Hope this clears things up for you. :)