A piece and ham is the same Scottish plainness as the piece and cheese, built around a slice of cooked ham instead of a slab of cheese. In broad Scots a "piece" is a sandwich, the thing taken to work or school in a poke, and a piece and ham is that thing reduced to its baseline: bread, butter, and one slice of ham, named in the dialect that carries it. The word does as much work as the filling. This is the Scottish lunchbox standard, the sandwich every other piece is measured against, and its quality is decided entirely by how good the ham is and how honestly it is put together.
The craft is the counterweight and the bread. Cooked ham is salty and faintly fatty, so the build wants a sharp note to cut it, mustard or a smear of pickle, applied in a measured stripe rather than a flood that soaks the bread. Butter goes edge to edge and is not optional: it carries the salt across to the plain wheat and seals the crumb so the pickle's vinegar does not soften it before the morning is out. The bread is soft plain loaf, white or brown, because a piece is a carrier and there is nowhere for a tired ham or a mean scrape of butter to hide. Cut in half, wrapped, and pressed flat in a poke, it is built for a pocket and a shift, which is exactly why a good one is made with care.
The variations stay inside the single-filling frame. Ham and mustard is the standard, ham and pickle the sweeter alternative, ham and tomato the version that brings a little moisture and acid back in. Its nearest relative is the piece and cheese, the same plain piece built around a slab of cheese, and the wider cold-cut shelf of corned beef, luncheon meat, and tongue runs the same logic with a different cure. Those deserve their own article rather than being crowded in here.