Both mean "to leave" but when do you use one instead of another ? Does 出発する implies "leaving and go on a trip" ? Or maybe is one more formal than the other ?
出発 refers specifically to departure. 出る, meanwhile, just generally means to go out, to come out, and could be used in reference to belly buttons, dresser drawers, stepping out into the yard, going onstage, or leaving a bathtub, among other potential contexts. You'd never use 出発する for leaving the bathtub, unless you're being silly. For heading out onto the town, or to do errands, etc., a better verb might be 出かける.