If you want to know about usage, I would use the word, BERATE, to describe a mother severely scolding her child. For example, a mother might say in a loud and upset voice, "Never, never do that again! Never cross the road without looking both ways!' I would use the word REBUKE to describe a teacher reproving a student. For example, the teacher might say in perhaps a calmer but definitely authoritative voice, "You will not be given another chance to improve your marks!" Hope this helps

Just an additional note -- both words are not commonly used in conversational American English, anymore. I do hear forms of "berate" every once in awhile.

no difference. A dictionary search shows this clearly.