agony vs pain

agony and pain both are nouns.

Word	Noun	Adjective	Verb	Adverb
agony	Yes	No	No	No
pain	Yes	No	Yes	No

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

Other hypernyms of agony include hurting.

agony (noun)	pain (noun)
intense feelings of suffering; acute mental or physical pain	a somatic sensation of acute discomfort
a state of acute pain	something or someone that causes trouble; a source of unhappiness
	emotional distress; a fundamental feeling that people try to avoid
	a symptom of some physical hurt or disorder

agony (verb)	pain (verb)
	cause bodily suffering to and make sick or indisposed
	cause emotional anguish or make miserable