The Heads of sub Schools (these replaced my role as Deputy Headmaster), the counselling staff, Matron or the other nursing staff – there’s a lot of options a student can exercise if they feel they’ve been given an unfair detention. When corporal punishment is used, we have to deal with realities imposed by the desire to administer it in a timely fashion that don’t apply with any other punishments.
From an objective viewpoint, the adults’ definition probably is better than a child’s but the child’s subjective view is what’s going to affect her (or his) behaviour. If I had been given a punishment that I thought was unfairly harsher than that given to my “partner in crime”, I would have strongly resented that and reacted accordingly. That some research showed my punishment was, theoretically, more lenient wouldn’t cut any ice.