Not that it means anything, but Googled the differences and this paragraph came up on some Chelsea site. Pretty much what my thoughts on what the differences are too.
'By these definitions a fan is someone that has an interest or admiration for a sport, art form or famous person – i.e. highlighting the often passing interest in something rooted in attraction, personalities or entertainment whereas a supporter is someone who is actively interested in (i.e. goes to games) and wishes success for a particular team (i.e. gets behind them in the hope that they will succeed)!'