Depending on the martial art that you're studying, no, you don't get a black belt and it stops there. Just like the pre-black belts, there are rankings. Usually you start at 10th Kyu (kyu being beginner or amateur) and work down to 1st Kyu. Then you hit 1st Dan (dan being master), which is the beginning of black belts. Then you work your way back up towards 10th Dan (not many of those anywhere in any discipline). There is no stopping.
The idea of different degrees of Saints is a pretty good parallel, though.
(I'm not a black belt, but both my parents are.)