do up vs wrap

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

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

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

Other hypernyms of do up include wrap up.

do up (noun)	wrap (noun)
	cloak that is folded or wrapped around a person
	the covering (usually paper or cellophane) in which something is wrapped
	a sandwich in which the filling is rolled up in a soft tortilla

do up (verb)	wrap (verb)
use special care in dressing, making-up, etc.	arrange or fold as a cover or protection
wrap for decorative purposes	enclose or enfold completely with or as if with a covering
	arrange or coil around
	crash into so as to coil around