hurt vs pain

hurt and pain both are nouns.

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

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

Other hypernyms of hurt include painfulness.

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

Other hypernyms of hurt include painfulness.

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

Other hyponyms of hurt include injure, wound, ail, trouble, disagree with.

As verbs, hurt and pain are synonyms defined as:

Other synonyms of hurt include anguish.

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

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

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