buy vs pay off

buy is a noun but pay off is not a noun.

Word	Noun	Adjective	Verb	Adverb
buy	Yes	No	Yes	No
pay off	No	No	Yes	No

As verbs, pay off is a hyponym of buy; that is, pay off is a word with a more specific, narrower meaning than buy:

Other hyponyms of buy include sop, buy off.

buy (noun)	pay off (noun)
an advantageous purchase

buy (verb)	pay off (verb)
accept as true	take vengeance on or get even
obtain by purchase; acquire by means of a financial transaction	eliminate by paying off (debts)
make illegal payments to in exchange for favors or influence	pay someone with influence in order to receive a favor
acquire by trade or sacrifice or exchange	yield a profit or result
be worth or be capable of buying	pay off (loans or promissory notes)
	do or give something to somebody in return