detriment vs damage

detriment and damage both are nouns.

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

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

Other hypernyms of detriment include harm, impairment.

detriment (noun)	damage (noun)
a damage or loss	the act of damaging something or someone
	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

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