chastisement vs punishment

chastisement and punishment both are nouns.

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

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

Other hypernyms of chastisement include penalisation, penalization, penalty.

chastisement (noun)	punishment (noun)
verbal punishment	the act of punishing, or the infliction of a penalty
a rebuke for making a mistake