acetaminophen vs painkiller

acetaminophen and painkiller both are nouns.

Word	Noun	Adjective	Verb	Adverb
acetaminophen	Yes	No	No	No
painkiller	Yes	No	No	No

As nouns, painkiller is a hypernym of acetaminophen; that is, painkiller 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)
painkiller: a medicine used to relieve pain

Other hypernyms of acetaminophen include analgesic, anodyne, pain pill.

acetaminophen (noun)	painkiller (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