brush up vs polish

brush up is not a noun while polish is a noun.

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

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

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

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

brush up (noun)	polish (noun)
	the property of being smooth and shiny
	a highly developed state of perfection; having a flawless or impeccable quality
	a preparation used in polishing

brush up (verb)	polish (verb)
bring to a highly developed, finished, or refined state	bring to a highly developed, finished, or refined state
refresh one's memory	improve or perfect by pruning or polishing
	make (a surface) shine