At my school there was no singular term for a caning where the headmaster himself would refer to it as a ‘good thrashing’ as in what ‘you need my boy is a good hard thrashing’
Some masters would just refer to it as ‘a caning’ while others ‘a beating’ and the boys would describe it as any of those three with a few individual terms such as ‘a striping’ or a even ‘the high jump’ but generaly after returning from the heads office when enquired upon by young and inquisitive minds it would usualy be ‘I got the cane’ or ‘I got the stick’ while the more ‘snobbish’ would say ‘I was beaten’ or I was given a thrashing’
This also applied when describing the number of strokes