A just means he does it in general. B means he's doing it right now (i.e. he's doing something right now that is related to this activity).
To give another concrete example, I would say that I make bracelets as a hobby. But I currently am not making bracelets. However, if I were to go buy supplies for that and someone were to ask what it's for, I would say at that time that I'm making bracelets. Make sense?
So similarly, you would use B if the guy in question is looking at his change, or mentioning the year a coin was made, or doing something else related to his presumed coin collecting.
EDIT: You can also use B to point out that he's proactive about it at the present even if he's not actively doing it at this time. This one is more complicated, though, so I'm not quite sure how to explain it.