The gammon sandwich is the cured-ham-steak sandwich, and the thing that sets it apart is the cut of meat, not the build. Gammon is cured pork from the hind leg, the same primal as ham, but it is sold and cooked as a thick steak rather than sliced thin off a cooked joint, so it eats with a denser, meatier bite and carries the salt of the cure deeper into the muscle. A gammon sandwich is that steak, cooked and then laid in bread, and it reads quite differently from a ham sandwich made of folded carved slices: heavier, firmer, saltier, closer to eating a small piece of cooked meat between bread than to a deli filling. The base is the whole foundation, and the named gammon sandwiches are all this steak plus one variable laid on top of it.
The craft is managing the cure and the density against plain bread. Gammon is intensely salted, so the steak is usually cooked through, grilled or fried until the fat catches, and then either kept in a slab for a firm, sliceable bite or cut down so it is not a single tough plank between soft slices. The bread is kept soft and plain to carry a strong, dense filling rather than argue with it, and butter on the bread is structural here, sealing the crumb and bridging the heavy salt of the cure across into the wheat so the sandwich does not read as one briny note. The meat can go in warm from the pan or cold and set; warm keeps the fat slack and the steak tender, cold firms it for a packed-lunch sandwich. Either way the salt is the thing the rest of the build is answering.
The variations are defined by what is set against that salt, and each earns its own name for the counter it brings. A fried egg adds a soft yolk that runs into the meat as a sauce; a ring of pineapple brings a sweet acid that cuts straight through the cure; mustard or a sharp pickle does the same job in a drier register. The wider roast and Sunday-dinner shelf, cold roast pork, ham off the bone, sits alongside it as the same cured-and-cooked-pork instinct in a different cut. Each deserves its own article rather than being crowded in here.