Hi, Ryan!
Irse is to leave, as in: Me voy, no me quedo más. Where you're going to is irrelevant. Otherwise you'd say: yo voy al cine (non reflexive). It has the sense of not staying in a place any longer.
Salir is to go out. Salgo a las 8:00 para mi trabajo. Hoy no salgo, me quedo en casa sounds really similar but they are not the same. No salgo is I'm not going out.
Does this help?
lidia