I was looking at parts to connect a speedlight + umbrella etc. to a light stand, and I (link) saw a zoo of types: B,C,E,EII, EIII, maybe F (or is that the other end?), and Google didn't turn up a guide to them. I'm hoping someone here can explain.
Looks like you're looking at umbrella swivels on eBay. Those designations don't really mean anything--they're not a naming standard, and there doesn't seem to be a whole lot of differences among them. The main styles generally are whether it's compact with a knob, or the more traditional size with a handle, and then there are more variants for a) holding a flash on its side rather than upright, and b) mounts that can hold multiple speedlights. Whether it comes with or without the stud might be another characteristic. The foot that holds the flash or the angle of the umbrella shaft hold may change, but they pretty much all work the same way. And those letter designations simply seem to be a way for the seller to keep track of which model they're selling.
This is a simple mechanical linkage to connect a speedlight to the lightstand. The pictures of the swivels pretty much tell you what you need to know.