medicine vs drug

medicine and drug both are nouns.

Word	Noun	Adjective	Verb	Adverb
medicine	Yes	No	Yes	No
drug	Yes	No	Yes	No

As nouns, drug is a hypernym of medicine; that is, drug is a word with a broader meaning than medicine:

medicine: (medicine) something that treats or prevents or alleviates the symptoms of disease
drug: a substance that is used as a medicine or narcotic

As verbs, drug is a hyponym of medicine; that is, drug is a word with a more specific, narrower meaning than medicine:

Other hyponyms of medicine include dose, salve.

medicine (noun)	drug (noun)
the learned profession that is mastered by graduate training in a medical school and that is devoted to preventing or alleviating or curing diseases and injuries	a substance that is used as a medicine or narcotic
punishment for one's actions
(medicine) something that treats or prevents or alleviates the symptoms of disease
the branches of medical science that deal with nonsurgical techniques

medicine (verb)	drug (verb)
treat medicinally, treat with medicine	administer a drug to
	use recreational drugs