Bacon and tattie scone is the Scottish answer to the question of what to do with bacon at breakfast, and the answer puts a potato scone inside the roll rather than using it as the roll. A tattie scone is a thin, soft, griddle-cooked round of mashed potato and flour, flat and pliable, fried until its surface takes a little colour. In this build it goes in alongside the bacon, folded into a soft morning roll, so the sandwich is carrying two starches with very different jobs: the roll is the soft, absorbent wrapper and the tattie scone is a dense, savoury, fried layer inside it. That internal potato slab is the defining component, the thing that makes this a named Scottish sandwich rather than a bacon roll with a regional accent.
The build works because the two starches are doing opposite things on purpose. The tattie scone is fried, often in the bacon fat, so its surface firms and browns and it brings a soft but substantial potato body to the centre of the roll, soaking up rendered fat and yolk without falling apart. The bacon is cooked until the fat has rendered and the edge crisped, giving a salty, firm counter to the soft scone so the inside of the roll is not uniformly soft and starchy. The morning roll, well-fired or plain, is the soft outer carrier and it still gets buttered, because unlike the all-potato-bread build there is a leavened crumb here that needs sealing against fat and against the moisture the scone carries. The result is heavier and more filling than a plain bacon butty by design: the tattie scone is there to make a small amount of bacon into a full breakfast in one hand, which is exactly the job it does inside the Scottish fry it comes from.
The variations are the Scottish breakfast this belongs to and the regional carriers that mirror it. A fried egg is the usual addition, its yolk binding the bacon and the scone; Lorne sausage, the square sliced sausage, often joins or replaces the bacon in the same roll; black pudding is the other common fry component folded in. The Northern Irish potato bread is the closest relative across the water, a different region's fried potato carrier for the same filling. Each of those deserves its own article rather than being crowded in here.