anaesthetic vs drug

anaesthetic and drug both are nouns.

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

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

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

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

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