The stottie cake sandwich is named for its bread and stands on it, because the stottie is the whole reason the sandwich exists as its own thing. A stottie, or stottie cake, is a Northeast bread out of Newcastle and the wider region: a large, flat, round loaf, dense and chewy with a close pale crumb and a soft floury crust, baked heavy rather than risen light. The defining fact of the sandwich is what that density allows. Soft white bread sets a hard limit on how wet and how heavy a filling can be before the slice gives way; a stottie has the structure to carry a generous, moist, substantial load without collapsing, so the sandwich is built around the bread's strength rather than around the filling's restraint.
The craft is matching the load to a bread that can take one. A stottie is split or wedged thick and filled hand, often with ham, pease pudding, saveloy, bacon, or a full fried breakfast, because the chewy crumb can hold a filling that would turn ordinary white to paste before lunch. That same density is a constraint as well as a licence: a stottie is firm to bite, so the filling is kept soft and well moistened, with butter or a sauce supplying the lubrication a heavy bread would otherwise make hard going. It is best eaten the day it is made, when the crumb is still tender rather than tightening as it stales, which is part of why the stottie sandwich reads as a fresh, local, bakery thing rather than a chiller one. The bread is the flavour and the structure both, and the filling frames it rather than the other way round.
The variations are the fillings the bread can carry rather than departures from it, and the canonical Northeast pairing is ham and pease pudding, the soft yellow split-pea spread bedded against cooked ham in the split stottie. Saveloy and stuffing, bacon and sausage, or a savoury fried-breakfast load each use the same dense round as the carrier. Other named regional breads, the barm, the cob, the bap, run the same bread-is-the-story logic in their own towns. Each deserves its own article rather than being crowded in here.