pain vs agonize

pain is a noun but agonize is not a noun.

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

As verbs, agonize is a hyponym of pain; that is, agonize is a word with a more specific, narrower meaning than pain:

Other hyponyms of pain include break someone's heart, agonise, try, excruciate, rack, torment, torture.

pain (noun)	agonize (noun)
a somatic sensation of acute discomfort
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

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