brush up vs polish up

brush up and polish up both are verbs.

Word	Noun	Adjective	Verb	Adverb
brush up	No	No	Yes	No
polish up	No	No	Yes	No

As verbs, brush up and polish up are synonyms defined as:

brush up and polish up: bring to a highly developed, finished, or refined state

Other synonyms of brush up include polish, round, round off.

brush up (verb)	polish up (verb)
bring to a highly developed, finished, or refined state	bring to a highly developed, finished, or refined state
refresh one's memory