gift wrapping vs wrapper

gift wrapping and wrapper both are nouns.

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

As nouns, wrapper is a hypernym of gift wrapping; that is, wrapper is a word with a broader meaning than gift wrapping:

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

Other hypernyms of gift wrapping include wrap, wrapping.

gift wrapping (noun)	wrapper (noun)
ornamental wrapping for gifts	cloak that is folded or wrapped around a person
	a loose dressing gown for women
	the covering (usually paper or cellophane) in which something is wrapped