penalty vs chastisement

penalty and chastisement both are nouns.

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

As nouns, chastisement is a hyponym of penalty; that is, chastisement is a word with a more specific, narrower meaning than penalty:

penalty (noun)	chastisement (noun)
the act of punishing, or the infliction of a penalty	verbal punishment
the disadvantage or painful consequences of an action or condition	a rebuke for making a mistake
(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