finish off vs wrap up

finish off and wrap up both are verbs.

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

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

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

finish off (verb)	wrap up (verb)
finish a task completely	clothe, as if for protection from the elements
	form a cylinder by rolling
	finish a task completely
	arrange or fold as a cover or protection