expense vs detriment

expense and detriment both are nouns.

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

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

Other hypernyms of expense include hurt.

expense (noun)	detriment (noun)
a detriment or sacrifice	a damage or loss
amounts paid for goods and services that may be currently tax deductible (as opposed to capital expenditures)
money spent to perform work and usually reimbursed by an employer

expense (verb)	detriment (verb)
reduce the estimated value of something