You call it spanking, or slapping on the bum.
Hitting colloquially gives the impression of a closed-fist.
> seems odd to have the person in authority return the favor by hurting the kids as punishment
The world is not fair. You can pick and choose rules based on a moral code but things like dress code, drugs, etc. are the institutional rules and they have setup consequences, agree with them or not.
And if you're hurting the child you aren't spanking, you're beating.