At the top is a ribeye steak with the back rib bone still attached. Below is a boneless rib roast, pretty much the same muscle with the bone removed.

Back ribs: The meat is between the bones

Back ribs are popular for barbecue, but I am not a big fan. I suspect their popularity is because they are cut from some expensive steaks and back ribs are popular pork cuts.

The ribeye steak is among the most expensive cuts of beef, and that's a back rib on the left of the steak in the photo. The ribeye is a fabulous hunk of meat that is tender and juicy, in my humble opinion the best meat on the cow. Ribeyes lie in the dorsal area, on top of rib bones near the spine, towards the front of the animal, just behind the shoulder.

As you move further towards the midsection of the animal, the steak on top of the ribs is called the strip steak or shell steak, another highly desirable cut. Sometimes the ribeye has a smaller round hunk of meat on the other side of the rib bone, the filet mignon, another highly desirable cut. If the filet and the ribeye are both there on either side of the rib bone, you have a porterhouse steak. If it is from further back and there is a strip steak with a small filet, you have a T-bone steak. These are all first-rate steaks and very expensive.

Ribeyes and strip steaks are often sold boneless which leaves the back rib bones available for sale separately. The bones usually are 6-8" long, slightly curved, with very little meat on top and a nice finger of meat between them. Why so little meat on top? Because it is so valuable the steaks are cut "to the quick" off the bone, leaving little meat behind. The bones often show through, and are called "shiners". They usually come in sections of about seven bones.

Back ribs are good for braising because the marrow is a stupendous source of flavor for stews, and they are popular for barbecue, but they are not my favorite cut for barbecue because they have so little meat and they must be cooked to well done to be made tender.

Short ribs: The meat is
on top of the bones

The best cut of beef ribs comes from the lower, ventral, section, from the 6th through 10th rib, roughly the same cut as the St. Louis cut of pork ribs. It is called the short plate, and the ribs are called short ribs not because they are short in length, but because they come from what is called the short plate. The short plate is located right in front of another inexpensive, chewy but flavorful cut, the flank steak, and just behind another favorite cut for barbecue, the brisket.

The bones are almost straight and they have 1-2" of meat on top. They are good for barbecue, kalbi, and braising. Shorties are my favorite cut for barbecue because it is possible to cook them medium rare. That's the temp at which beef is most flavorful.

Short ribs are cut several ways:

English Cut Short Ribs

Shown below, this is the most common cut. There are usually 4-5 bones from 3-8" long. They can be sold as a rack or as a package of individual ribs. This is the way I like to buy them. The slab is about 7" x 8" and about 1" to 2" thick.

Short ribs often have a layer of fat on top, although some butchers remove it. This cut, about 9" x 5" is typical. Notice the meat is not all the same thickness, ranging from 1 - 2" thick.	This is the same slab of English Cut Short Ribs shown from above with the fat cap removed. The meat is wonderfully marbled, which means big flavor. The meat is thicker on one side from near the shoulder and those are called chuck ribs sometimes. They're the best.
Here is the same slab bone side up. You can see the thin leathery membrane which should be removed.

Flanken Cut Short Ribs

Flanken cut rib bones are typically only 1/2" to 1" long and they are popular in Asian and Mexican groceries. There is a lot of hard fat but the meat absorbs marinades well and is tasty if grilled. Try the Korean Kalbi marinade. This cut is also good braised. and I've even cut it off the bone and used it for stir fry.

Short Rib Riblets

Often shorties are sold in individual bone sections ranging from 1" to 6" long. Here is a typical riblet, a section of a single bone about 2" long and 1.5" wide. These are very versatile and they're great for braising, for slow cookers, for barbecue, and for Korean Kalbi. Just try to select a package with meaty hunks. Butchers usually try to hide sections that are mostly fat among the good ones.

Boneless Short Ribs

You can occasionally buy boneless rib meat cut off the bone. The cut on the left was about 1/2" thick and 8" long when I bought it. The cut at right was about 2" thick and 8" long. Both cuts work well on the grill but they can be tough at high temps. I recommend a Jaccard meat tenderizer.

If you can't buy boneless rib meat, you can remove it from the bone yourself. With a fileting knife, cut the meat off the bone, trim the thick silverskin and thick fat from the top, and remove the connective tissue from the bottom. You will have slabs of beautiful meat and super bones for soup or stock.

Dino Ribs

If you want something really showy, ask your butcher for Dino Ribs. These are short ribs 12" or more long. They're a special order, and a special meal.

Buying short ribs

Buying short ribs requires attentiveness. There are often 1/4" thick veins of fat running through the muscle layers, so you need to inspect the package carefully. Butchers seem to like slipping a nasty one or two in each package like the section of flanken cut at tight.