The intent is explicitly and specifically to punish someone and be a punishment.

Compensatory damages are awarded in an attempt to compensate the plaintiff for the damage they received due to the actions of the defendant. Punitive damages are awarded to the plaintiff on top of the compensatory damages and their exact purpose is to punish the defendant for their actions.

They are two different types of damages and the exact purpose of punitive damages is to be a punishment. It's their raison d'etre. They were created to provide further levers to punish people.