I agree I think there is a slight difference between authority and power - authority is closely related to power, but they're not exactly the same. Like our military and police are raw power. An elected sheriff is granted authority (and with it power) but the sheriff loses that power once he's no longer sherif. And he doesn't gain it from direct power, he doesn't have to beat up the strongest cop, but rather everyone agrees that he SHOULD have that power. There's probably a better way to explain this but I think there is a difference.