analgesic vs pain pill

analgesic and pain pill both are nouns.

Word	Noun	Adjective	Verb	Adverb
analgesic	Yes	Yes	No	No
pain pill	Yes	No	No	No

As nouns, analgesic and pain pill are synonyms defined as:

Other synonyms of analgesic include anodyne, painkiller.

analgesic (noun)	pain pill (noun)
a medicine used to relieve pain	a medicine used to relieve pain

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