clear up vs polish off

clear up and polish off both are verbs.

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

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

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

clear up (verb)	polish off (verb)
free (the throat) by making a rasping sound	finish a task completely
finish a task completely	finish eating all the food on one's plate or on the table
make free from confusion or ambiguity; make clear	kill intentionally and with premeditation
make clear and (more) comprehensible
become clear