The corned beef sandwich is decided at the tin, and the first decision is how you cut it. Tinned corned beef is salt-cured beef cooked and pressed into a brick of lean fibre and rendered fat, and it can go into bread two ways. A slab cut straight from the tin gives a dense, sliceable plank that holds its shape and eats firm and salty in a clean square. Flaked apart with a fork it goes loose and fibrous, packs into the bread, and spreads the salt and fat across every bite instead of delivering it in one block. The whole character of the sandwich follows from that choice: the slab is structured and the flake is yielding, and a good corned beef sandwich commits to one rather than landing somewhere mushy in between.
The craft is managing salt and fat against plain bread. Corned beef is intensely seasoned and the cured fat softens and slicks the moment it sits between two warm slices, so the bread is kept soft and plain to carry it rather than compete, and butter on the bread is structural here, sealing the crumb and bridging the salt to the wheat. The meat is not heated; it is laid cold and firm so the fat stays set and the slab keeps its edge. A corned beef sandwich with nothing to push against it reads as one long salty fatty note, which is why the form almost always reaches for a sharp counter, and why its own variations are defined by what that counter is.
The variations are a question of the cutting agent and they earn their own names for it. Corned beef with raw onion adds a sharp allium bite straight against the fat. Corned beef with Branston or another vinegary pickle cuts the richness with sweet acid. Corned beef hash, the meat fried with potato until it crisps and then folded into bread, turns the cold cut into a hot leftover entirely. Each of those is a different sandwich built on the same brick, and they deserve their own articles rather than being crowded in here.