wrap vs wrap up

wrap is a noun but wrap up is not a noun.

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

As verbs, wrap and wrap up are synonyms defined as:

wrap (noun)	wrap up (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

wrap (verb)	wrap up (verb)
arrange or fold as a cover or protection	clothe, as if for protection from the elements
enclose or enfold completely with or as if with a covering	form a cylinder by rolling
arrange or coil around	finish a task completely
crash into so as to coil around	arrange or fold as a cover or protection