hairstyle vs coif

hairstyle and coif both are nouns.

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

As nouns, hairstyle and coif are synonyms defined as:

hairstyle and coif: the arrangement of the hair (especially a woman's hair)

Other synonyms of hairstyle include coiffure, hair style, hairdo.

hairstyle (noun)	coif (noun)
the arrangement of the hair (especially a woman's 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 arrangement of the hair (especially a woman's hair)

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