acetaminophen vs pain pill

acetaminophen and pain pill both are nouns.

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

As nouns, pain pill is a hypernym of acetaminophen; that is, pain pill is a word with a broader meaning than acetaminophen:

acetaminophen: an analgesic for mild pain but not for inflammation; also used as an antipyretic; (Datril, Tylenol, Panadol, Phenaphen, Tempra, and Anacin III are trademarks of brands of acetaminophen tablets)
pain pill: a medicine used to relieve pain

Other hypernyms of acetaminophen include analgesic, anodyne, painkiller.

acetaminophen (noun)	pain pill (noun)
an analgesic for mild pain but not for inflammation; also used as an antipyretic; (Datril, Tylenol, Panadol, Phenaphen, Tempra, and Anacin III are trademarks of brands of acetaminophen tablets)	a medicine used to relieve pain