haircut vs crew cut

haircut and crew cut both are nouns.

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

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

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

haircut (noun)	crew cut (noun)
the act of cutting the hair	a closely cropped haircut; usually for men or boys
the style in which hair has been cut