purchase vs buy

purchase and buy both are nouns.

Word	Noun	Adjective	Verb	Adverb
purchase	Yes	No	Yes	No
buy	Yes	No	Yes	No

As nouns, buy is a hyponym of purchase; that is, buy is a word with a more specific, narrower meaning than purchase:

Other hyponyms of purchase include stock buyback, bargain, steal.

As verbs, purchase and buy are synonyms defined as:

purchase and buy: obtain by purchase; acquire by means of a financial transaction

purchase (noun)	buy (noun)
the acquisition of something for payment	an advantageous purchase
the mechanical advantage gained by being in a position to use a lever
a means of exerting influence or gaining advantage
something acquired by purchase

purchase (verb)	buy (verb)
obtain by purchase; acquire by means of a financial transaction	accept as true
	obtain by purchase; acquire by means of a financial transaction
	make illegal payments to in exchange for favors or influence
	acquire by trade or sacrifice or exchange
	be worth or be capable of buying