Prime rib is not a specific cut of beef, but rather the preparation used for a beef rib roast. Unlike with other cuts of beef, the word "prime" in regards to prime rib does not refer to a specific grade of beef.
Prime rib is a rib roast. When shopping for a rib roast, it is important to know that they are available in two styles. The small end is cut from the loin section, making it more tender and less fatty. The large end is cut from the chuck section, and it can be tougher than the small end. Because the small cut comes from the more tender part of the beef, it is usually more expensive than roasts cut from the large end. The large end rib roast also contains more fat and muscle than the small end roast.