haircut vs coif

haircut and coif both are nouns.

Word	Noun	Adjective	Verb	Adverb
haircut	Yes	No	No	No
coif	Yes	No	Yes	No

As nouns, coif is a hypernym of haircut; that is, coif is a word with a broader meaning than haircut:

Other hypernyms of haircut include coiffure, hair style, hairdo, hairstyle.

haircut (noun)	coif (noun)
the act of cutting the hair	a skullcap worn by nuns under a veil or by soldiers under a hood of mail or formerly by British sergeants-at-law
the style in which hair has been cut	the arrangement of the hair (especially a woman's hair)

haircut (verb)	coif (verb)
	arrange attractively
	cover with a coif