Someone who battles or brawls with other people is a fighter. Some fighters, like boxers, do it professionally, while others just have a tendency to fight.
If you have a habit of getting into scuffles or fistfights, you're a fighter, and when you watch a boxing match, you might pick one of the two fighters to root for. An animal might also be described as a fighter: lions are natural fighters, and a fish struggling hard on the end of a hook is a fighter. Other fighters work heroically for a belief or ideal: "She was a fighter in the struggle for civil rights."