brush up vs perfect

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

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

As verbs, perfect is a hypernym of brush up; that is, perfect is a word with a broader meaning than brush up:

Other hypernyms of brush up include hone.

brush up (noun)	perfect (noun)
	a tense of verbs used in describing action that has been completed (sometimes regarded as perfective aspect)

brush up (adjective)	perfect (adjective)
	being complete of its kind and without defect or blemish
	precisely accurate or exact
	without qualification; used informally as (often pejorative) intensifiers

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