The ham salad sandwich is the bare ham sandwich with its single flaw addressed, and the flaw it addresses is dryness. Cooked ham on buttered bread is salty and faintly fatty but texturally one note, and the salad is what introduces water and crunch back into a filling that has none of its own. Lettuce, cucumber, tomato, sometimes sliced raw onion or grated carrot, go in with the ham, and their job is structural before it is decorative: they carry moisture into a dry stack and a snap against a soft one. The defining decision is therefore not the ham, which is constant, but how much wet vegetable the bread can take before the whole thing collapses, and a good ham salad sandwich is the one that has solved that arithmetic rather than the one that has piled the most in.
The craft is moisture control, and it is unforgiving because every component the salad adds is also a way for the sandwich to fail. Tomato bleeds, cucumber weeps, lettuce wilts under a warm slice of ham, so the vegetables are kept on the dry side, the tomato is salted and drained or laid against the ham rather than the crumb, and the butter spread to the edges waterproofs the bread against what does escape. The lettuce goes in crisp and dry as a barrier as much as a leaf, and the salad is built up rather than crushed flat so it keeps some structure under the press. The bread stays soft and plain so it yields to a delicate filling instead of fighting it, and the balance the cook is aiming for is a ham sandwich with the dry corner replaced by something cool and alive, not a salad that happens to contain ham.
The variations are a question of what binds and what sharpens. A smear of salad cream or mayonnaise turns the loose salad into something that holds together and adds a tang the plain build lacks. Ham with the salad plus a stripe of mustard or pickle stacks an acid edge onto the moisture. The same logic runs under every other salad sandwich on the British counter, cheese salad and chicken salad chief among them. Each deserves its own article rather than being crowded in here.