I would consider the majority to be demitasse cups. They are very short, while a classic shave mug is about the same size as a coffee mug. The reference sites don't reveal the one I once had, with straight sides, and a medium height, medium width. The "tall" Old Spice mug I have is a ceramic, not milk glass, and shows on the reference site as being offered as a coffee cup. It is very heavy, very thick-walled, and holds more than a coffee mug does. I use mine for shave soap.
I also have one with a black glaze, that I use for shave soap, it is shorter, less heavy in weight.
If a photo is wanted, I'm overdue to photograph the lot of them . . we'll see about that ("soon").