I think that the cane is a particularly English instrument of punishment. A good, fresh rattan cane, imported from Malaysia, is a remarkable thing. Fearful to be on the receiving end. For it cuts, and bites, and bruises. I find it almost unbearable, and need to be tethered and helpless. Otherwise I would run away!
To hold a cane in one's hand, feeling its whippiness and strength, is superb. The sound it makes cutting through the air is unique, and an important part of the whole experience.
Usually a cane is longer and more flexible than a riding crop or a dressage whip, and therefore needs more skill. Otherwise the strokes can roam far and wide.