wrap up vs gift-wrap

wrap up and gift-wrap both are verbs.

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

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

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

wrap up (verb)	gift-wrap (verb)
clothe, as if for protection from the elements	wrap (a gift) attractively
form a cylinder by rolling
finish a task completely
arrange or fold as a cover or protection