The smoked bacon butty is the ordinary butty with one variable turned up, and that variable is the smoke. The assembly is unchanged: back bacon, a soft floured roll, butter, a stripe of brown or red sauce. What separates this from a plain or green-bacon butty is that the rasher has been cured and then hung over smoke, oak or beech, so it carries a second savour on top of the salt of the cure. That smoke is the defining decision. It is laid down long before the bread, and it is the reason a smoked butty reads as darker and more insistent than the same sandwich built from an unsmoked rasher next to it.
The craft is the same heat and grease management every butty demands, with the smoke setting the proportions. Smoked back bacon is already loud, so the cook is hot and short, the fat rendered and the edge crisped without driving the smoke into bitterness. The roll is soft enough to take a little of the rendered dripping without collapsing, and buttered so the salt is carried across to the wheat rather than left sitting on top of it. The sauce question, brown or red, stays a genuine divide, but it is applied sparingly and inside the roll, because smoked bacon is the strongest thing in the sandwich and a flood of sauce only buries the smoke the whole thing is built around. Restraint everywhere else is what lets the cure speak.
The variations all turn on the cure and the cut rather than the assembly, which is why each earns its own name. The unsmoked or green rasher is cleaner and more directly porky, the smoke removed entirely. A dry-cure under the smoke fries harder and concentrates the savour, where a wet-cure steams softer before it crisps. The streaky cut against the back cut changes the fat-to-meat ratio and so changes how the smoke and the crisp land in the bite. Each deserves its own article rather than being crowded in here.