gift-wrap vs wrap

gift-wrap is not a noun while wrap is a noun.

Word	Noun	Adjective	Verb	Adverb
gift-wrap	No	No	Yes	No
wrap	Yes	No	Yes	No

As verbs, wrap is a hypernym of gift-wrap; that is, wrap is a word with a broader meaning than gift-wrap:

Other hypernyms of gift-wrap include wrap up.

gift-wrap (noun)	wrap (noun)
	cloak that is folded or wrapped around a person
	the covering (usually paper or cellophane) in which something is wrapped
	a sandwich in which the filling is rolled up in a soft tortilla

gift-wrap (verb)	wrap (verb)
wrap (a gift) attractively	arrange or fold as a cover or protection
	enclose or enfold completely with or as if with a covering
	arrange or coil around
	crash into so as to coil around