mistress vs courtesan

mistress and courtesan both are nouns.

Word	Noun	Adjective	Verb	Adverb
mistress	Yes	No	No	No
courtesan	Yes	No	No	No

As nouns, courtesan is a hyponym of mistress; that is, courtesan is a word with a more specific, narrower meaning than mistress:

mistress: an adulterous woman; a woman who has an ongoing extramarital sexual relationship with a man
courtesan: a woman who cohabits with an important man

Other hyponyms of mistress include concubine, doxy, paramour.

mistress (noun)	courtesan (noun)
a woman master who directs the work of others	a woman who cohabits with an important man
an adulterous woman; a woman who has an ongoing extramarital sexual relationship with a man
a woman schoolteacher (especially one regarded as strict)