One group is led by Prof. Charles Xavier, a.k.a. Prof. X, who is played by Patrick Stewart. He recruits, teaches and leads a group of mutants who try to co-exist with and protect mankind from evil. The second band of mutants is led by Erik Magnus Lehnsherr, a.k.a. Magneto. They're known as the Brotherhood of Evil Mutants.
Nothing subtle there.
Magneto is portrayed by Ian McKellen. Erik is haunted by boyhood memories of being torn away from his parents at Auschwitz, a Nazi concentration camp. That memory is graphically established in the opening scene. Magneto believes that history will inevitably repeat itself, so he isn't surprised when the Senate debates the virtues of a Mutant Registration Act. Magneto believes that legislation is the forerunner of a new holocaust and he isn't waiting to become a victim again.