The Scotch pie sandwich is the pie eaten between plain sliced bread, and the flat carb framing is what sets it apart from the roll version. A Scotch pie is a small double-crust pie of seasoned mutton in a stiff hot-water-crust shell, baked straight-sided with a low lid. Pressed between two slices of soft white loaf rather than cupped in a roll, the same pie reads differently: the bread folds flat against the curved shell, the pie is often opened or crushed slightly so it spreads to the bread's footprint, and the result is wider and shallower than the deep, hand-filling roll. The defining fact is the same as the roll's, a complete pie carried inside more carbohydrate, but the geometry changes the eating. Sliced bread presses the pastry rather than surrounding it, and the sandwich is something you fold and bite across rather than something you hold whole and work down.
The craft is heat and stopping the bread going to paste. The pie goes in hot so the mutton fat stays liquid and the pastry stays short. Sliced bread is thinner-walled than a roll and soaks faster, so buttering it to the edges is not optional: the butter waterproofs the crumb against the grease and any gravy and bridges the pie's salt to the wheat. Because flat slices give the pie nothing to brace against, the pie is usually pressed or partly broken so it grips the bread and does not slide out as a whole disc when the sandwich is lifted. The bread is soft and plain because the pastry already supplies all the structure and a crusty loaf would fight a shell that is firm on its own. Brown sauce in a stripe is the acid that cuts the fatty, peppery filling.
The variations are Scotland's baked shelf met with the same crushed-into-bread logic. The bridie folds seasoned beef in pastry; the macaroni pie and the mince pie change the filling in the same shell; the pie supper sets it against chips. The Scotch pie roll, the pie set whole inside a soft roll rather than pressed between slices, is the close cousin with a different carbohydrate frame. Each of those deserves its own article rather than being crowded in here.