Anacin III vs painkiller

Anacin III and painkiller both are nouns.

Word	Noun	Adjective	Verb	Adverb
Anacin III	Yes	No	No	No
painkiller	Yes	No	No	No

As nouns, painkiller is a hypernym of Anacin III; that is, painkiller is a word with a broader meaning than Anacin III:

Anacin III: 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 Anacin III include analgesic, anodyne, pain pill.

Anacin III (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