chastisement vs penalty

chastisement and penalty both are nouns.

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

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

Other hypernyms of chastisement include penalisation, penalization, punishment.

chastisement (noun)	penalty (noun)
verbal punishment	the act of punishing, or the infliction of a penalty
a rebuke for making a mistake	the disadvantage or painful consequences of an action or condition
	(games) a handicap or disadvantage that is imposed on a competitor (or a team) for an infraction of the rules of the game
	a payment required for not fulfilling a contract