recuperate vs cure

recuperate is not a noun while cure is a noun.

Word	Noun	Adjective	Verb	Adverb
recuperate	No	No	Yes	No
cure	Yes	No	Yes	No

As verbs, cure is a hypernym of recuperate; that is, cure is a word with a broader meaning than recuperate:

Other hypernyms of recuperate include bring around, heal.

recuperate (noun)	cure (noun)
	a medicine or therapy that cures disease or relieve pain

recuperate (verb)	cure (verb)
get over an illness or shock	provide a cure for, make healthy again
restore to good health or strength	prepare by drying, salting, or chemical processing in order to preserve
regain a former condition after a financial loss	be or become preserved
regain or make up for	make (substances) hard and improve their usability