The Western, also called the Denver, is an omelet that has been engineered into a sandwich, and the engineering is what separates it from eggs served beside toast. Ham, onion, and bell pepper are cooked into beaten eggs as a single bound slab rather than scrambled loose, because the egg has to hold together as a structural layer that can be lifted between two slices of bread. The filling is the omelet itself: the egg is both the protein and the binder that locks the ham and the diced pepper and onion into one liftable mass. Cook it loose and it is breakfast on bread; cook it as a set slab and it is the Denver.
The craft is in the cook and the fit. The egg is taken just to set, kept tender rather than rubbery, and shaped to the footprint of the bread so the sandwich has clean edges and does not shed filling on the first bite. The ham is diced small and given a quick sear so it renders a little salt and char into the egg rather than sitting in it cold; the onion and green bell pepper are cut fine and cooked just enough to soften their raw bite while keeping a trace of crunch, which is the only textural counter in an otherwise soft build. The bread is plain toast, deliberately: a firm, dry slice that braces the moist egg slab and keeps the sandwich from going limp, with nothing assertive enough to argue with the filling.
The variations are small and mostly about heat and bread. The hot griddle-counter version serves it open-face under a little melted cheese; the cold cut-and-wrapped version is built to travel and eaten at room temperature; the roll version trades the toast for a soft bun and a thicker egg slab. Each belongs to the wider American lunch-counter tradition where a few honest ingredients are correctly proportioned, and each keeps the ham-onion-pepper-and-egg core while changing one element around it, and each deserves its own article rather than being crowded in here.