kept woman vs courtesan

kept woman and courtesan both are nouns.

Word	Noun	Adjective	Verb	Adverb
kept woman	Yes	No	No	No
courtesan	Yes	No	No	No

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

kept woman: 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 kept woman include concubine, doxy, paramour.

kept woman (noun)	courtesan (noun)
an adulterous woman; a woman who has an ongoing extramarital sexual relationship with a man	a woman who cohabits with an important man