User blog comment:The ehhhMAZING deathstroke!/idk/@comment-28140789-20160429061052

In the storyline, Superman/Regime (the Superman of the Injustice dimension) stops being a "boy scout" after a plot by the Joker causes him to kill his pregnant wife. Superman murders him and quite a few others, and takes over the world (hence 'regime', a ruling government, though not usually used in a world-encompassing context), taking a hardline on crime and law enforcement and the necessity of peace, all to the extent of not leaving any sovereignty or dissent elsewhere in the world.

Regime characters are allied to him and native to his dimension. Insurgency characters are native to the dimension and oppose him (an 'insurgency' being a rebellion, and usually one not as powerful as the ruling order). "Prime" characters are those who are native to the main dimension of the comics. Effectively the "Prime" characters that actually go into the Injustice dimension (Joker I think is the only villain that crosses over) prove the muscle needed to overthrow the Regime.