Most ancient Greek games, including the Olympic Games, had 3 separate competitions of combat sports, wrestling, pankration and pugilism. Some people competed in more than one of them, so pugilism was usually scheduled to be the last of the 3, because otherwise those injured in pugilism would not have been able to compete in the following competition.

Pankration allowed striking, kicking, wrestling and submission grappling, so it was very similar to the MMA of today.

However, the pankration fighters did not bandage their hands with leather straps, like the pugilists, so they were not able to hit as hard the head of the opponent.

Moreover, they had plenty of other options for winning a match, so striking was not as emphasized as in pugilism, which remains true today in MMA vs. boxing.