The terms represent two very distinct beliefs about the job of teaching children. The belief behind punishment is that pain must be felt for learning to take place. The child may learn to fear getting caught and to avoid repeating the same behavior, if the punishment is severe. For punishment to be effective, it must be severe, and the severity must increase with subsequent infractions. The child learns nothing of real-life consequences and grows up without the ability to discipline himself.
Punishment is for hurting, discipline is for training.
Choose an action, receive the consequence. We are all responsible for our actions. We are all held accountable for our choices. We must discipline ourselves. An action is discipline if it creates a positive learning process for the child.