Movie Clips are one of the most powerful symbols in Flash. They can have script on themselves in AS2.0, but not in AS3.0. Movie Clips can be animated. Movie Clips can also usually be seen as a flash movie of its own.
The usage of this symbol is pretty self-explanatory. They can also have script on themselves in AS2.0, but not in AS3.0.
Graphics are the most basic symbol in Flash. They can't have script on themselves, and they can't have filters or can't have an instance name.