Sea-Doo is a derivative of Ski-Doo. Both are made by Bombardier Recreational Products; the Sea-Doo is a “personal watercraft,” and the Ski-Doo is a snowmobile. The Ski-Doo came first, and I’m guessing the name is a pun on “twenty-three skidoo”, which Wikipedia says originally referred to “leaving quickly”, something like “skedaddle”. Obviously, a snowmobile allows one to travel quickly over the snow.
So the etymology appears to be Skedaddle -> 23 Skidoo -> Ski-Doo -> Sea-Doo.
(Edit: I’m wrong! Wikipedia says the Ski-Doo was originally supposed to be called the “Ski-Dog”, but someone made a typo and they stuck with it! So much for my attempt to reconstruct a derivation!)
Jet Ski is also a trademark used by Kawasaki for their personal watercraft. It was designed by the same guy who designed the Sea-Doo for Bombardier.
