Punir vs. châtier
In French, 'punir' and 'châtier' both mean 'to punish', but they are often used in different contexts and carry slightly different connotations.
Punir
This verb is used in a general sense to indicate the action of imposing a penalty or sanction on someone for an offense or misbehavior. The term is not historically rooted in physical punishment and can refer to any kind of punitive measure.
Les parents doivent parfois punir leurs enfants pour les aider à distinguer le bien du mal.
(Parents sometimes have to punish their children to help them tell right from wrong.)
Le juge a décidé de punir le criminel avec plusieurs années de prison.
(The judge decided to punish the criminal with several years in prison.)
L'école a des règles strictes, et les étudiants qui ne les respectent pas seront punis.
(The school has strict rules, and students who don't follow them will be punished.)
Châtier
'Châtier' implies a more severe or harsh punishment, often with a moral or corrective intention. It may also carry a historical or literary connotation, referring to archaic or religious forms of punishment.
Dans l'histoire, les rois châtiaient les traîtres avec une grande sévérité.
(In history, kings would punish traitors with great severity.)
Certains pensent que la société devrait plus sévèrement châtier les délits financiers.
(Some believe that society should more harshly punish financial crimes.)
"Qui aime bien châtie bien", dit le proverbe, suggérant que l'on peut être dur dans la punition par bienveillance.
("Spare the rod and spoil the child" is a proverb suggesting that one can be tough in punishment out of kindness.)
Summary
'Punir' is more commonly used to refer generally to the act of punishing and is neutral regarding the severity or method of punishment. On the other hand, 'châtier' often indicates a harsher, more severe form of punishment with moral underpinnings, and can sound archaic or formal due to its historical usages.