I’d imagine that the headmaster would do the proper paperwork after administering a severe, formal six whacks for some grievous offence, but the geography teacher would be more likely to “forget” to record that he had given someone one on the hand for larking around in his lesson.
In most state schools, the cane (or the strap) was the only permitted form of corporal punishment — whacks with the slipper or the bunsen burner tube or the teachers hand were never really “legal”. So of course they went unrecorded. The teachers may have thought that they were too trivial to be worth writing down. I seem to recall my primary school headmaster telling parents that there was hardly any corporal punishment at his school, because he had only used the cane twice in the last year. He didn’t mention that almost every day there was a queue of boys outside his office waiting to me smacked, quite hard, on the back of the legs or the bottom, and that some of the teachers kept “unofficial” slippers in their desks or put boys over their knees for an “unofficial” slap. None of which was ever recorded in any book.