St. Louis-style ribs are a variation of the full slab.
They are trimmed and have the brisket bone removed.
Kansas City-style ribs are another variation.
They are trimmed even more than the St. Louis style ribs and have the hard bone removed.
Baby back ribs, sometimes called loin ribs, are cut from the loin section.
They are shorter and smaller than spareribs.
They have a covering of meat over the bones and also between them.
Because they do come from the loin, they are leaner and meatier than spare ribs.
They are also considerably more expensive and in shorter supply.
Country-style Spare ribs are actually not ribs at all but are cut from the blade end of the loin, right behind the upper portion of the pork shoulder.
They are more like fatty pork chops than ribs.
While they have more fat per pound than any of the other styles of ribs, the fat is in layers and the meat between those layers is leaner and less marbled than most other ribs.
They are the meatiest of all the ribs.