coif vs hairstyle

coif and hairstyle both are nouns.

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

As nouns, coif and hairstyle are synonyms defined as:

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

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

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

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