Can they be used interchangeably?
Oars come in pairs and are used for rowing. A paddle is very much like an oar, but it is used with two arms, going to either side of the boat for direction.
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It sounds like you call the rowing pole for a canoe an aor and for a kayak a paddle. Is my understanding correct?
Is an oar latched to the boat therefore you don't need both arms to handle it?
Another observation, the verb that goes with an oar is row while paddle goes with paddle and not row. Is my understanding correct?
Yes, I would agree. You row with an oar, but you paddle with a paddle.
Someone who does skulling will have to comment on that sport. I only know about canoes and kayaks.
The technical difference between and oar and a paddle is that an oar requires a fulcrum attached to the boat whereas a paddle uses one of the paddler's two hands as the fulcrum. Oar and paddle are not not synonomous us in spite of what crossword composers think.
This is incorrect. Oars do not necessarily come in pairs (see sweep versus sculling). In sweep, oars are used with two arms too. The main difference is that the oar is connected to the boat (via oarlock) and paddle is not. This drives the difference in the technique that propels the motion.