finish vs polish off

finish is a noun but polish off is not a noun.

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

As verbs, polish off is a hyponym of finish; that is, polish off is a word with a more specific, narrower meaning than finish:

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

finish and polish off: finish eating all the food on one's plate or on the table

Other synonyms of finish include eat up.

finish (noun)	polish off (noun)
the act of finishing
a decorative texture or appearance of a surface (or the substance that gives it that appearance)
(wine tasting) the taste of a wine on the back of the tongue (as it is swallowed)
designated event that concludes a contest (especially a race)
the downfall of someone (as of persons on one side of a conflict)
event whose occurrence ends something
the place designated as the end (as of a race or journey)
a highly developed state of perfection; having a flawless or impeccable quality
the temporal end; the concluding time

finish (verb)	polish off (verb)
finally be or do something	finish a task completely
come or bring to a finish or an end	finish eating all the food on one's plate or on the table
cause to finish a relationship with somebody	kill intentionally and with premeditation
finish eating all the food on one's plate or on the table
provide with a finish
have an end, in a temporal, spatial, or quantitative sense; either spatial or metaphorical