Egg and salad cream is the egg sandwich with the binder swapped, and the swap is the whole sandwich. Everywhere else the bound-egg filling is held with mayonnaise, a thick, fatty emulsion that coats the egg and reads rich. Salad cream is a different thing: thinner, sharper, and sweet-sour from its vinegar and mustard, a pourable dressing rather than a spreadable one. Put it through chopped egg and the result is not a slightly different egg mayonnaise. It is a looser, tangier, brighter filling where the acidity, not the fat, is the leading note, and the egg tastes lifted and clean rather than padded. That is why the binder is named on the sandwich. It is not a substitute for mayonnaise; it produces a different sandwich from the same egg.
The craft is managing a thin binder against a soft filling. Salad cream carries more water and less fat than mayonnaise, so it is used with a more careful hand: enough to coat and season the egg, not so much that the filling goes wet and slides, because there is no thick emulsion here to hold the structure together and a heavy pour will soak straight through the bread. The egg is chopped a touch coarser to give the loose dressing something to cling to, seasoned in the bowl with salt and white pepper, and the bread is buttered firmly to the edges so the crumb is sealed against a filling that is, by design, on the wet and acidic side. Pressed and cut soon after building, because a salad-cream bind does not sit as patiently as a mayonnaise one.
The variations are the rest of the bound-egg family separated by what holds it and what cuts it. Egg mayonnaise is the rich, default version with the fatty binder; egg and chive keeps mayonnaise but adds an allium edge; egg and cress adds a peppery shoot to the same base. The salad-cream and mayonnaise versions of cheese run the same split a shelf over. Each deserves its own article rather than being crowded in here.