I wanna expand on this just a little bit.
"Respect my authority" means to bow down before my position over you.
"Respect my person" means to respect that I have needs and desires just like every other person.
One is spoken from a place of dominance, wanting obedience. The other is spoken from subservience, wanting the same kind of life as the dominant one has for the same amount of work being put in.
They both acknowledge the inequality, but the authoritarian position says "I don't care."
@KitsuneAlicia They say respect has to be earned, not demanded. Otherwise it is obedience.