Cult and cult following are both derived from the latin 'cultus', adoration, care. Still I have the feeling that 'cult' is used for (rather strong) enthusiam of a relatively homogeneous and large group of people, and of a more temporary character; another aspect of 'cult' seems to me that it's related to films that are mainstream nor middle brow, so neither Peter Jackson nor Woody Allen can be called cult. And it certainly isn't avant garde.
The chop choy movies, Bruce Lee and the likes, were cult in the early seventies; I guess there are still people devoted to them, but they have become very rare: in Holland some ten or twelve Shaw brother movies were released, and they weren't particularly succesful, in fact they became dead stock very soon. (I saw Bruce's The Big Boss for 2,99 € this morning).
To have a cult following, is an expression that has - to me - a less temporary, more structural meaning; the group of people worshiping the movie(s) usually is very variable (moviegoers, critics, filmmakers, reverends, philosophers) and the movie(s) can be pulp, mainstream, any kind of brow or even avant garde. Jackson, Allen, Leone, Tati, Fellini, Tarantino, they all can have a cult following.