Even if nobody knows what it is, there must be some difference. So getting back to the OP I would say that I would not even attempt putting the i337 firmware on an i337m. That's asking for potential problems. I saw some stuff about rooting that was for Canadian models only.
I still, after all these posts, (I may have missed it) can't figure out who the carrier was supposed to be as the model numbers other than the International, (unlocked) numbers are pretty carrier specific. No answer as to who the phone was purchased from AFAIK.