This was a series of studies where participants were instructed to administer electric shocks to another person (who was actually an actor). The experiment demonstrated high levels of obedience to authority figures even when it involved harming another person.
Authoritarian Personality: This is a personality type characterized by extreme obedience and unquestioning respect for and submission to the authority of a person external to the self. Such individuals would likely show high levels of obedience in situations like those created in Milgram's or Zimbardo's experiments.
Compliance involves changing one's behavior due to the request or direction of another person, not necessarily an authority figure. It differs from obedience which specifically involves orders from someone in a position of power.