detention vs punishment

detention and punishment both are nouns.

Word	Noun	Adjective	Verb	Adverb
detention	Yes	No	No	No
punishment	Yes	No	No	No

As nouns, punishment is a hypernym of detention; that is, punishment is a word with a broader meaning than detention:

detention: a punishment in which a student must stay at school after others have gone home
punishment: the act of punishing, or the infliction of a penalty

Other hypernyms of detention include penalisation, penalization, penalty.

detention (noun)	punishment (noun)
a punishment in which a student must stay at school after others have gone home	the act of punishing, or the infliction of a penalty
a state of being confined (usually for a short time)