anesthetic vs drug

anesthetic and drug both are nouns.

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

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

anesthetic (noun)	drug (noun)
a drug that causes temporary loss of bodily sensations	a substance that is used as a medicine or narcotic

anesthetic (adjective)	drug (adjective)
relating to or producing insensibility
characterized by insensibility

anesthetic (verb)	drug (verb)
	administer a drug to
	use recreational drugs