In archaic terms the difference between mistress and courtesan
is that
mistress is used as the title of a married woman before her name. Now used only in the abbreviated form
Mrs while
courtesan is a woman of a royal or noble court.
As nouns the difference between mistress and courtesan
is that
mistress is a woman, specifically one with great control, authority or ownership while
courtesan is a woman of a royal or noble court.