painkiller vs medicament

painkiller and medicament both are nouns.

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

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

painkiller: a medicine used to relieve pain
medicament: (medicine) something that treats or prevents or alleviates the symptoms of disease

Other hypernyms of painkiller include medication, medicinal drug, medicine.

painkiller (noun)	medicament (noun)
a medicine used to relieve pain	(medicine) something that treats or prevents or alleviates the symptoms of disease