Dilaudid vs painkiller

Dilaudid and painkiller both are nouns.

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

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

Dilaudid: a narcotic analgesic (trade name Dilaudid) used to treat moderate to severe pain
painkiller: a medicine used to relieve pain

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

Dilaudid (noun)	painkiller (noun)
a narcotic analgesic (trade name Dilaudid) used to treat moderate to severe pain	a medicine used to relieve pain