I made the following comments about water wheels in a Facebook post and will make them again here: In my almost lifetime "career' of looking at nineteenth and early twentieth century steamboat plans and specs I have noted that the wheels were always referred to as "waterwheels". When and how this changed to "paddlewheels" I don't know and probably never will. In Europe the side wheel boats were/are referred to as "paddle steamers" or just "paddlers". (For example, the British "Waverly"is advertised as the last ocean-going paddle steamer.) Their bucket planks (paddles) are called "buckets" or "floats". This is also true of East Coast U.S. steamers. I would guess that the "waterwheel" terminology originated with grist mills which were waterwheel powered and those waterwheels had buckets which caught the flowing water causing the wheel to turn. Probably many of the early steamboat builders had experience with grist mill construction, so the terminology was transferred to steamboat building.

Well, this is all just trivia in todays world and I'm not losing any sleep over it.