finish off vs polish off

finish off and polish off both are verbs.

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

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

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

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