The roast beef sandwich is the plain national reading, the baseline against which every regional version is a deliberate deviation. Strip away the jus of Chicago, the dipping cup of Los Angeles, the onion roll and barbecue sauce of the Massachusetts North Shore, and what remains is the thing itself: sliced roast beef on bread, with horseradish or one of a small set of sauces. It is defined by its restraint. There is no codified bread, no required heat, no signature soak. The sandwich is whatever a good piece of roast beef and a few honest accents make it, and that lack of a gimmick is exactly what makes it the reference point for all the builds that have one.
The craft, with nothing to hide behind, comes down to the beef and the cut. A roast cooked to a rosy medium-rare and rested keeps its juice; sliced thin against the grain it stays tender, while a thick or with-grain slice turns chewy no matter how good the roast was. The bread is a choice rather than a rule: a soft sliced loaf for a cold deli build, a kaiser or a sturdier roll when the pile is heavier, each picked to carry the meat without overwhelming it. Horseradish is the classic sharp counter, with the heat and acid to lift a rich, mild meat; mayonnaise adds fat, a sharp mustard adds bite, and a slice of cheese, when used, binds the pile to the bread. Served cold it is a clean, simple thing judged entirely on the quality of three or four ingredients. Served warm, with the beef gently heated and the juices kept light, it leans toward the family of hot beef builds without committing to any one region's method.
The variations are the regional sandwiches that each took this baseline and added a single defining move. The Chicago Italian beef soaks the roll in seasoned jus; the Los Angeles French dip serves that jus on the side; the North Shore build dresses cold rare beef in James River sauce on an onion roll; beef on weck leans on a salt-and-caraway roll and horseradish; the chain roast beef standardized a thin-sliced version on a soft bun. Each of those is its own discipline and deserves its own article rather than being crowded in here.