wrap up vs garment

wrap up is not a noun while garment is a noun.

Word	Noun	Adjective	Verb	Adverb
wrap up	No	No	Yes	No
garment	Yes	No	Yes	No

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

Other hypernyms of wrap up include apparel, clothe, dress, enclothe, fit out, garb, habilitate, raiment, tog.

wrap up (noun)	garment (noun)
	an article of clothing

wrap up (verb)	garment (verb)
clothe, as if for protection from the elements	provide with clothes or put clothes on
form a cylinder by rolling
finish a task completely
arrange or fold as a cover or protection