haircut vs brush cut

haircut and brush cut both are nouns.

Word	Noun	Adjective	Verb	Adverb
haircut	Yes	No	No	No
brush cut	Yes	No	No	No

As nouns, brush cut is a hyponym of haircut; that is, brush cut is a word with a more specific, narrower meaning than haircut:

Other hyponyms of haircut include butch, crew cut, flattop, mohawk, mohawk haircut.

haircut (noun)	brush cut (noun)
the act of cutting the hair	a short haircut with hairs standing up like a brush
the style in which hair has been cut