The difference between a Ribeye Roast and a Rib Roast is that the Ribeye is boneless and the Rib Roast has rib bones. This cut comes from the top of the rib primal cut, with the meat on the outside of the ribs. The bones removed for Ribeye are the Back Ribs.
this is a one of the tenderest roasts you can serve, and easy to slice if it is boneless, but, being loin meat, it is not the most flavorful.
Rib Roasts can be of substantial size, 3-1/2 to over 18 pounds, depending on size of cow and how it is cut. The full Rib Roast can be so large it is often cut into two sections, called the First Cut or Small End Cut which includes ribs 9 or 10 through 12, and Second Cut or Large End Cut which includes ribs 6 through 8 or 9. The photo specimen was small and short at 9 x 5 x 2-1/2 inches and 3 pounds 10 ounces.
More on Cuts of Beef.