I do see a distinct difference between fan and supporter. A supporter offers support to a club, be that by paying to attend matches, buying merchandise, or volunteering for the club. A fan, may well care for a club as much as anyone else, follow results, team selections, performances etc, but they don't actually offer any support to the club. When the Premier League 'plastics' in my office claim to 'support' Arsenal or whoever, I always wonder in what way they are actually 'supporting' them. Most just 'support' Sky.