penalty vs punishment

penalty and punishment both are nouns.

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

As nouns, penalty and punishment are synonyms defined as:

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

Other synonyms of penalty include penalisation, penalization.

penalty (noun)	punishment (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