perfect vs polish up

perfect is a noun but polish up is not a noun.

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

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

Other hyponyms of perfect include optimise, optimize, brush up, polish, round, round off.

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

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

perfect (verb)	polish up (verb)
make perfect or complete	bring to a highly developed, finished, or refined state