Almost, but not exactly. Prime rib is cut from the prime, superior portion of the animal, where the meat is especially tender and well-marbled. It includes ribs 6 through 12. Prime rib is sometimes called a standing rib roast because the bones enable it to stand upright for roasting. But if you cut the meat away from the bones, leaving the "eye" (the large central muscle) and a layer of fat, then that's a ribeye roast. Some say that it's best to cook bone-in roasts because the bones produce a juicier and more flavorful roast. It's true that the meat portions closest to a bone-in steak, for example, taste the best. But it's also true that it's difficult to get to them unless you're willing to gnaw on bones! That's why many home cooks, myself included, prefer to cook a ribeye roast. It is smaller, and you can carve it easily since there are no bones. It is still very flavorful, and the fat cap is sublime.