finish up vs polish off

finish up and polish off both are verbs.

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

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

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

finish up (verb)	polish off (verb)
finish a task completely	finish a task completely
finally be or do something	finish eating all the food on one's plate or on the table
	kill intentionally and with premeditation