coif vs hair style

coif and hair style both are nouns.

Word	Noun	Adjective	Verb	Adverb
coif	Yes	No	Yes	No
hair style	Yes	No	No	No

As nouns, coif and hair style are synonyms defined as:

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

Other synonyms of coif include coiffure, hairdo, hairstyle.

coif (noun)	hair style (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)	hair style (verb)
arrange attractively
cover with a coif