hurt vs damage

hurt and damage both are nouns.

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

As nouns, hurt and damage are synonyms defined as:

Other synonyms of hurt include harm, scathe.

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

Other hypernyms of hurt include harm, impairment.

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

hurt (noun)	damage (noun)
the act of damaging something or someone	the act of damaging something or someone
a damage or loss	any harm or injury resulting from a violation of a legal right
feelings of mental or physical pain	the occurrence of a change for the worse
psychological suffering	loss of military equipment
any physical damage to the body caused by violence or accident or fracture etc.; the condition of an injury	the amount of money needed to purchase something

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

hurt (verb)	damage (verb)
give trouble or pain to	inflict damage upon
be in pain	suffer or be susceptible to damage
cause damage or affect negatively
hurt the feelings of
cause emotional anguish or make miserable
be the source of pain
feel physical pain