Ping-pong requires a paddle but isn't played on water.
Paddleball also requires a paddle and isn't played on water, but isn't necessarily a sport.
Padel is a racquet sport in the US and Canada
A sport which requires water to be played.
A kayak paddle will have two blades, and you paddle by pulling each through the water in turn. A canoe paddle just has the one blade, and you paddle by pulling it through the water on alternate sides of your craft.
Water polo and water volleyball are sports played with a ball in a pool.
You paddle with an oar. If you are talking about paddle wheels, the wheel turns because of the bucket boards. The boards dip in the water and turn.
There is Swimming, Water Polo, Diving, and Water Aerobics.
A paddling pool is a pool, usually inflatable, which has enough water to paddle as opposed to swim.
They do the doggy paddle