wrap vs gift wrapping

wrap and gift wrapping both are nouns.

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

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

wrap: the covering (usually paper or cellophane) in which something is wrapped
gift wrapping: ornamental wrapping for gifts

Other hyponyms of wrap include envelope, film, plastic film, jacket, plastic wrap.

wrap (noun)	gift wrapping (noun)
cloak that is folded or wrapped around a person	ornamental wrapping for gifts
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 wrapping (verb)
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