I actually interchange them. It all depends on who I am spending my time with and chatting with. If I am chatting with my friends from WOW I say toon where it originated from because lets be honest... the whole of wow's world looks like a cartoon. When I play any other MMO I usually say character or my character's name that I am referencing. My character name has been Leedora since EQ 1 so I just refer to her as Lee or Leedora just like everyone else who knows me does lol.
Honestly, I could care less what version you use to describe it. Neither option bothers me, hence why I interchange them and use whatever matches the people I am chatting with. If Bob always says toon then I will say that so that he understands what I mean, while if Tim says character then I will use that term, but mainly for me its just always Lee =)