ponytail vs coif

ponytail and coif both are nouns.

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

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

ponytail: a hair style that draws the hair back so that it hangs down in back of the head like a pony's tail
coif: the arrangement of the hair (especially a woman's hair)

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

ponytail (noun)	coif (noun)
a hair style that draws the hair back so that it hangs down in back of the head like a pony's tail	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)

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