Motivation. A fanatic will be motivated by a cause which is also supported by others who are not fanatics, for example nationalism or politics. What makes them fanatics is that they are more extreme in their action. The motives of a "nutter" are much more personal - and of course their actions might not even be extreme, just out of the ordinary.

It's perfectly possible to be both at the same time. There have been several episodes recently where those involved, while having sort of rational motivation, have had significent mental problems.

It's not a clear distinction with some "causes" that most people would see as pretty crazy, such as racism and some kinds of religious fundamentalism.