punishment vs penalty

punishment and penalty both are nouns.

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

As nouns, punishment and penalty are synonyms defined as:

punishment and penalty: the act of punishing, or the infliction of a penalty

Other synonyms of punishment include penalisation, penalization.

punishment (noun)	penalty (noun)
the act of punishing, or the infliction of a penalty	the act of punishing, or the infliction of a penalty
	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