wrap vs gift-wrap

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

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

As verbs, gift-wrap is a hyponym of wrap; that is, gift-wrap is a word with a more specific, narrower meaning than wrap:

Other hyponyms of wrap include do up, parcel, cere, shrinkwrap, shroud.

wrap (noun)	gift-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

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