I don't think anyone specifically said "paddling", though if they did I might have grouped it with whipping/caning(/flogging/cropping). When people say spanking in this fandom they seem to usually mean by hand.

I think when people say "coming untouched" they mean something the characters try to make happen intentionally... or, heck, maybe not, what do I know. Heh, there are enough fics where male characters have the mysterious ability to get 'instantly hard again' that it might not matter. (I saw a fic that had that the other day, and... no. Just no. Not unless it's literally magic.)