damage vs detriment

damage and detriment both are nouns.

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

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

Other hyponyms of damage include hurt, deformation, distortion, ladder, ravel, run.

damage (noun)	detriment (noun)
the act of damaging something or someone	a damage or loss
any harm or injury resulting from a violation of a legal right
the occurrence of a change for the worse
loss of military equipment
the amount of money needed to purchase something

damage (verb)	detriment (verb)
inflict damage upon
suffer or be susceptible to damage