I'd consider riding without a saddle to be bareback, regardless of whether you ride with a bareback pad. With that said, some of the more fancy bareback pads nowadays seem to be closer to riding with a saddle than riding bareback.
When I ride bareback, I prefer riding without any sort of pad. I tried a bareback pad once and it was extremely slippery, especially when it came to getting on the horse. I just felt unsafe.
My QH has the most awesome, broad back for bareback. He also has the bumpiest trot of any horse I've ever ridden. With him, the bumpy trot doesn't make it uncomfortable for me to ride, it just makes me fall off!