wrap up vs mop up

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

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

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

Other synonyms of wrap up include clear up, finish off, finish up, get through, polish off.

wrap up (noun)	mop up (noun)
	a concluding action

wrap up (verb)	mop up (verb)
clothe, as if for protection from the elements	finish a task completely
form a cylinder by rolling	defeat thoroughly
finish a task completely	to wash or wipe with or as if with a mop
arrange or fold as a cover or protection