The sausage biscuit is defined not by the sausage but by the carrier, and the carrier is a buttermilk biscuit that has to do something bread almost never does: stay tender while holding a hot, greasy patty. A good Southern biscuit is built on the deliberate undermixing of flour, fat, and buttermilk so it bakes up in flaky layers with a soft, fatty crumb. That crumb is the entire reason this sandwich is its own thing rather than a sausage patty on toast. Split warm, the biscuit's torn interior catches the rendered fat from the patty instead of shedding it, and the fat is what marries the two halves into a single bite.
The craft is in the biscuit and the patty's footprint. The biscuit dough is handled as little as possible and the fat kept cold, because overworked dough bakes dense and a dense biscuit fights a soft filling instead of cradling it. It is split while still warm so the steam has not set the crumb hard. The sausage is a seasoned fresh breakfast patty, sage-and-pepper forward, cooked on a flat-top and pressed to roughly the diameter of the biscuit so every bite has both and the structure stays even. There is usually nothing else: no cheese, no egg, no sauce in the plain build, because the point is the contrast between a salty, fatty, peppery patty and a bland, rich, yielding biscuit. Some hands add a thin smear of butter or a drop of hot sauce, and that is the whole assembly.
The variations are mostly additions to the same split-biscuit frame, and each pulls the sandwich toward a different breakfast. Add a folded egg and a slice of American cheese and it becomes the full sausage, egg, and cheese biscuit. Swap the sausage patty for fried country ham and it turns salt-forward and chewy; swap it for a fried chicken cutlet and it becomes the chicken biscuit that chains carried nationwide. The open-faced version smothered in sausage gravy is a close cousin built on the same biscuit. Each of those deserves its own article rather than being crowded in here.