wrap up vs do up

wrap up and do up both are verbs.

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

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

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

wrap up (verb)	do up (verb)
clothe, as if for protection from the elements	use special care in dressing, making-up, etc.
form a cylinder by rolling	wrap for decorative purposes
finish a task completely
arrange or fold as a cover or protection