The pasty bap is a Cornish and Devon oddity, and the thing that defines it is that the filling already has a complete crust before it ever meets the bread. A Cornish pasty is beef, potato, swede, and onion sealed inside a baked shortcrust shell with a rope crimp down one side, engineered to be a self-contained meal on its own. Splitting a soft bap and putting that whole baked pasty inside it is the entire move, and it is a deliberately redundant one: pastry inside bread, a sealed container placed inside a second carrier that the design never asked for. That redundancy is the point of the thing and the reason it stays a regional curiosity rather than a standard.
The craft, such as there is one, is the same carbohydrate-on-carbohydrate logic that runs through the chip butty and the pie barm, applied to a filling that needs no help. The bap is soft and plain because the pasty brings its own sturdy crust, its own seasoning, and its own structure, and a bread with any real chew would simply add a third layer of resistance to something already firm. Butter goes on the bap to lubricate a dry, dense, fully baked filling that has no sauce of its own and to stop the bread reading as an arid second crust. The pasty is usually warm when it goes in, because a cold baked pastry inside cold bread is two dry things with nothing to bind them, and warmth softens the crimp enough that the bap can press around it.
The variations are really just the pasty's own variations carried into bread. A cheese and onion pasty in a bap keeps the sealed-crust logic with a meat-free filling; a steak pasty makes it heavier; the wider pasty and pie family, the bridie, the Bedfordshire clanger, the pie barm, all share the engineered-container reasoning from their own regions. Each deserves its own article rather than being crowded in here.