pain vs hurt

pain and hurt both are nouns.

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

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

Other hyponyms of pain include growing pains, unpleasantness, mental anguish, suffering, distress, suffering.

As verbs, hurt is a hypernym of pain; that is, hurt is a word with a broader meaning than pain:

As verbs, pain and hurt are synonyms defined as:

Other synonyms of pain include anguish.

pain (noun)	hurt (noun)
a somatic sensation of acute discomfort	the act of damaging something or someone
something or someone that causes trouble; a source of unhappiness	a damage or loss
emotional distress; a fundamental feeling that people try to avoid	feelings of mental or physical pain
a symptom of some physical hurt or disorder	psychological suffering
	any physical damage to the body caused by violence or accident or fracture etc.; the condition of an injury

pain (adjective)	hurt (adjective)
	damaged; used of inanimate objects or their value
	suffering from physical injury especially that suffered in battle

pain (verb)	hurt (verb)
cause bodily suffering to and make sick or indisposed	give trouble or pain to
cause emotional anguish or make miserable	be in pain
	cause damage or affect negatively
	hurt the feelings of
	cause emotional anguish or make miserable
	be the source of pain
	feel physical pain