codeine vs analgesic

codeine and analgesic both are nouns.

Word	Noun	Adjective	Verb	Adverb
codeine	Yes	No	No	No
analgesic	Yes	Yes	No	No

As nouns, analgesic is a hypernym of codeine; that is, analgesic is a word with a broader meaning than codeine:

codeine: derivative of opium; used as an antitussive (to relieve coughing) and an analgesic (to relieve pain)
analgesic: a medicine used to relieve pain

Other hypernyms of codeine include anodyne, pain pill, painkiller, antitussive, opiate.

codeine (noun)	analgesic (noun)
derivative of opium; used as an antitussive (to relieve coughing) and an analgesic (to relieve pain)	a medicine used to relieve pain

codeine (adjective)	analgesic (adjective)
	capable of relieving pain