We always called the black and white spinner the beach ball and the colored one from OSX the pinwheel. May be a terminology thing, but I was talking about the old black and white spinner in MacOS. If one did any kind of video, image or 3d editing, it was not far behind and pretty much locked the computer up until whatever processing was done.

Classic MacOS also had a beach ball https://i.stack.imgur.com/sGdwO.png

It didn't plague the OS like it did in OS X though, usually it was accompanied by a progress dialog box.