the belt holster is designed to ride in a fixed position on your belt, always where you put it but sorta a pain to take on and off.
the paddle holster is designed to easily go on and come off, like for detectives who take off their guns in the stationhouse, the belt. the trade-off is that it slides back and forth along the belt, the early ones would even come off the belt during the draw.
the paddle needs to be wider than the holster to stabilize the gun at the waist line, to keep it from canting back and forth. a well designed paddle will use the hip to hold the holster in place. a really well designed paddle holster can be worn without a belt