Its purely a matter of opinion of course, but I tend to view a numismatist as an individual steeped in the relevant academia whereas a collector simply buys a coin because it looks nice, it has a historical connection, or what ever reason have you.
Not all collectors are numismatists and not all numismatists are collectors. Some are both. If you wanted to be a bit more strict, perhaps the line between the two can be drawn at actually publishing works on numismatics in a journal.
Another exception might be a coin dealer or employee. Its a complicated question 🙂