Ham paste is not a thinner ham sandwich; it is a different object that happens to start from pork. Sliced ham is a cut of meat laid whole between bread. Ham paste is cured cooked ham pounded with fat and seasoning into a smooth, pale, salty spread, sealed in a jar, and made to keep for months at the back of a cupboard with no refrigeration. Everything about how it is used follows from that shelf life. A paste built to survive unrefrigerated is concentrated to the point where its own salt and cure are the whole flavour, so it is used in the quantity of a condiment, not a filling. The defining fact is the ratio: this is a sandwich where the named ingredient is the thing you spread thinnest, and getting that thinness right is the entire skill.
The craft is the scrape and the butter under it. Ham paste is milder and lighter in colour than the beef and fish pastes on the same shelf, leaning on a gentle cure rather than a dark, aggressive one, but it is still salty and still texturally featureless, so it is dragged across the bread in a thin film rather than laid on in a layer. Butter is not optional lubrication here; it is the carrier that pulls the paste across the slice and stops a pale smear reading as a smear. The bread is soft and plain because the paste brings no texture of its own and a crust with real chew would have nothing in the filling to chew against. There is no heat, no acid, no second component: the sandwich is built cold, cut thin, pressed, and left in a tin until lunch, and like its potted relatives it sits well, the paste working into the crumb rather than weeping out of it.
The variations are a row of jars, not a row of recipes, and ham paste is one entry among them. Beef paste runs darker and more aggressively cured, chicken paste is paler and milder still, crab and salmon paste carry the same potted logic into fish, and bloater paste takes it to smoked herring. Each is the identical engineering met with a different protein, and each deserves its own article rather than being crowded in here.