gay woman vs butch

gay woman and butch both are nouns.

Word	Noun	Adjective	Verb	Adverb
gay woman	Yes	No	No	No
butch	Yes	Yes	No	No

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

Other hyponyms of gay woman include dike, dyke.

gay woman (noun)	butch (noun)
a female homosexual	a closely cropped haircut; usually for men or boys
	(slang) offensive term for a lesbian who is noticeably masculine

gay woman (adjective)	butch (adjective)
	(of male or female homosexuals) characterized by stereotypically male traits or appearance
	used of men; markedly masculine in appearance or manner