polish off vs finish off

polish off and finish off both are verbs.

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

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

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

polish off (verb)	finish 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