Detriment, n.
Etymology: [L. detrimentum, fr. deterere, detritum, to rub or wear away; de + terere to rub: cf. F. détriment. See Trite.]
1. That which injures or causes damage; mischief; harm; diminution; loss; damage; -- used very generically; as, detriments to property, religion, morals, etc. I can repair That detriment, if such it be. Milton.
2. A charge made to students and barristers for incidental repairs of the rooms they occupy. [Eng.]
Syn. -- Injury; loss; damage; disadvantage; prejudice; hurt; mischief; harm.
1 other Webster entry under this spelling
Detriment, v. t.
To do injury to; to hurt. [Archaic] Other might be determined thereby. Fuller.
Shades of meaning
Fernald has no entry of its own for detriment; he lists it under injury.
Where he writes about it:
Damage (L. damnum, loss) is that which occasions loss to the possessor; hence, any impairment of value, often with the suggestion of fault on the part of the one causing it; damage reduces value, utility, or beauty; detriment (L. deterere, to rub or wear away) is similar in meaning, but far milder. — from injury
Detriment may affect value only; damage always affects real worth or utility; as a rule, the slightest use of an article by a purchaser operates to its detriment if again offered for sale, tho the article may have received not the slightest damage. — from injury