Impact play, spanking, flagellation, all music to Queen Sensoria‘s ears. These terms, as well as many others, are all used to describe the art of hitting well.
More precise to the tool in use are the terms whipping, belting, flogging, paddling, caning, single-tailing and cropping; and to the part that is hits are spanking (buttocks) and slapping (face).
Over-the-knee spanking is also a common practice, as well as hairbrush spanking and faceslapping. Those 3 practices have a a charm of olden days about them that adds an interesting psychological aspect for some.