Mono is it's own runtime, like java. It mimics the .net runtime, but is not the same. Mono can be run on a huge number of systems, such as windows, OSX, Linux, and even things like the ps3 OS. Whereas the .net runtime works on windows and embedded windows only (ie the 360, phones, etc).
Generally you would compile an application to either mono or .net, and then you must distribute the installer for whichever runtime. That is a limiting factor even with mono, and can be kind of annoying. With unity, they package the mono runtime files of relevance right into the unity engine, which means no installation is needed and even if you have a different version of mono installed on your system, unity uses the version compiled into each game.
Hope that helps!