The butty is the same sausages as the bap, told in a different bread and a different register. Butty almost always means soft sliced white bread folded over, not a round roll, and that is the distinction worth leading with: where the bap is engineered to compress around the filling at a curved point, the butty lies flush against it along the whole flat face of two slices. Flatness changes how the thing behaves. A split fried banger pressed between two flat slices is gripped evenly across its entire length rather than at a single round arc, so the fat is spread into a broad band of crumb instead of pooling in the base of a roll, and the sandwich folds tight rather than holding a dome. The sausage is the constant every region agrees on; the butty is the variable, and the variable here is as much the word and the social register as the bread. Butty is the plain, unfussy, said-without-thinking term, the one that belongs to a works canteen or a kitchen at the end of a shift.
The build is the rendered-fat problem solved by the bread choice and by the cut. The sausage is fried all the way through so the interior bites cleanly rather than smearing, and the casing is browned because the caught skin carries the chew. It is split lengthways and laid flat, which lets it sit stable across two flat slices and present a browned cut face instead of rolling out between them. Butter spread to the edges of both slices is the structural part, sealing the soft crumb so the fat does not go straight through before the butty is eaten, a real constraint on a sandwich assembled in under a minute and held in one hand. The fold matters as much as the slices: pressed flat, the bread holds the sausages in a single even layer where a roll would let them shift, so the slices are chosen soft enough to yield to that press without tearing. The sauce, brown or red, goes inside against the meat and lands as soon as the fold closes.
The variations are the same filling under the other bread words and the breakfast around it. A sausage bap is the identical idea named for a soft round roll; a barm or a cob is the same again in other regions. A fried egg adds a yolk to manage, fried onions add a sweet counter, and the leftover Sunday version beds the sausages on mash. Each of those deserves its own article rather than being crowded in here.