ponytail vs hair style

ponytail and hair style both are nouns.

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

As nouns, hair style is a hypernym of ponytail; that is, hair style 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
hair style: the arrangement of the hair (especially a woman's hair)

Other hypernyms of ponytail include coif, coiffure, hairdo, hairstyle.

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