I first heard the terms...maybe five years ago. They're just a fancy way of trying to rename what, for 100 years, has been called rib steak.
The rib eye is a long round part of a beef that you can roll out of the front quarter by separating it with a knife. You get boneless rib eye steaks if you slice it before you cook it. If you roast it first and then slice it, you get prime rib, also boneless. When you don't roll it out, but saw the steaks directly from the quarter, you get a rib steak (with a rib bone).
When you look at a rib steak, you can see the round part that would have been a rib eye, but you also see an extra triangle of meat. Rib steaks are cheaper than rib eyes by the pound but usually it's about the same price per steak. The butcher knows a rib steak is not all meat and reduces the price per pound because of (1) the bone in there and also (2) because cutting with the band saw, rather than with a knife, is less labor intensive.
So, it appears that you get that meat triangle free. But wait there's more. When butchers rename them as hatchet style bone in rib eyes or tomahawk steaks, they can raise the prices.
EDIT: Removed extraneous characters created by system update.