The beef rib primal is from the forequarter of the steer and is essentially what remains after the chuck and short plate primals are removed.
Rib cuts are obtained from the cow's backbone and upper ribs.
The beef rib primal is found at the forequarter of the cow, behind the chuck (removed at the 5th/6th rib), above the short plate, and in front of the loin (removed at the 12th/13th rib).
Meaning, the beef rib primal contains meat from the 6th to the 12th rib - creating a few different cuts in between.
The rib primal offers some of the most prized cuts on the entire animal.
This fact is so true that the cross-section of the ribeye is one of the main factors used to evaluate the quality of beef.
Specifically, the longissimus dorsi muscle is analyzed at the 12th and 13th rib.
Beef is graded based on the marbling or intramuscular fat content found at this cross-section; The more visible fat found within the lean meat, the better the grade.
In the US, the grades are as follows (in descending order of quality): Prime, Choice, and Select.
Technically an entire rib primal contains rib bones that are up to 10 inches long at the chuck and 6 inches long at the loin.
However, when butchering, the bones are cut short (consumers aren't big on paying for something they can't eat). The remaining rib bones, all the way down to the sternum is part of the beef plate primal (beef short ribs).
Essentially, the rib primal is what remains after the chuck and beef short plate are removed.
There are a number of wonderful sub-primal cuts that come from this section of the steer.
Namely, the rib roast, various styles of beef rib steaks or ribeye steaks, ribeye cap roll, and beef back ribs.
A whole prime rib or "7-rib roast" can weigh anywhere from 14-22 lbs. Not only is this a lot of meat, it's also very expensive.
As a result, a Butcher will divide the roast into two smaller roasts, called a first and second cut.
It should be noted: This area of the steer is considered prime. It has a thick fat cap and heavily marbled meat. This is the reason prime is used, not necessarily because the meat is graded as prime.
Just to further confirm this fact, we can look at the United States Department of Agriculture (USDA) Food Standards and Labeling Policy handbook, where we're told:
PRIME RIB OF BEEF OR STANDING BEEF RIB ROAST FOR PRIME RIB:
These products do not have to be derived from USDA prime grade beef.USDA, Food Standards and Labeling Policy handbook, pg. 146.
The reason I bring this up is because several resources like to say that "Prime" is a legal designation and a "prime rib" can't be sold with that namesake if it's not actually graded as Prime by the USDA.
Yet, the folks who actually do the grading state the opposite.
The ribeye is a beef steak from the rib primal or the cylindrical muscle that is close to the steer's rib.
A true rib "eye" steak is just the center - the longismissus dorsi muscle - with the surrounding muscles and fat removed.
Today, ribeye is a catch-all term used to refer to this type of beef steak.
There are a few different ways to cut a ribeye steak. However, as a generalization, ribeye steak is either bone-in or boneless.
Note: While ribeye steaks are the same meat as prime rib, these cuts are cooked quite differently.
On every beef ribeye steak there is a cap. This part is also called the "deckle" or sometimes called the "calotte." Scientifically, it's the spinalis dorsi muscle.
In my opinion, it's the single best muscle on the entire steer.
This cap muscle can sometimes be removed from the entire 7-bone rib roast to create a beef ribeye roll; Where this muscle is physically rolled and held together with butcher's twine.
The beef back ribs are sourced from the dorsal area of the steer.
When these ribs are separated from the prime rib, the butcher attempts to keep the knife as close to the bone as possible. The reason for this is to maximize the weight of the ribeye steaks.
Beef back ribs are different from other types of beef ribs in that the meat is intercostal or between the bones as apposed to on top of the bone.
You can learn more about beef ribs in this article.
In the grand scheme of things, beef back ribs don't offer much in terms of meat yield, especially after cooking where the meat shrinks. However, for ribeye meat, they're usually quite affordable and make for an easy smoke for beginners.