T.I. vs. Floyd Mayweather -- Both Sides Posturing Over T.I.'s Mystery Punch

TMZ has sources close to both T.I. and Floyd Mayweather and it's become very clear ... each side is telling a very different version of events surrounding the fight.

No one is debating what caused it -- as TMZ first reported, it was over T.I.'s wife Tiny -- but what is up for debate ... is who hit whom during the melee.

T.I.'s side: Our T.I. sources say the rapper swung and hit Floyd ... which is what sparked the whole brawl at Fatburger in Las Vegas early Sunday morning. T.I. even hinted at the punch in an Instagram video he posted the next day.

Floyd's side: The champ is telling friends T.I. never hit him with any punch ... he only tussled with members of Floyd's security team.