The Chick-fil-A deluxe is the original sandwich with the parts the original deliberately leaves off: lettuce, tomato, and a slice of American cheese added to the pressure-fried fillet, toasted bun, and two pickles. The whole interest of the deluxe is what those additions do to a build that was engineered around restraint. The original is an argument that the fillet needs no company; the deluxe is the counter-argument, and reading the two side by side is the point of having both.
The craft is in how the extra layers change the sandwich's structure as much as its taste. The original keeps a tight, dry build so the smooth fried crust stays crisp from first bite to last. Adding cool tomato and lettuce introduces moisture and bulk that the simpler version carefully excludes, so the assembly order matters: the fillet sits hot against the toasted bun, the cheese goes on the warm fillet so it slumps and partially seals rather than sitting as a cold slab, and the wet produce is layered to one side so it does not steam the crust soft before the sandwich is eaten. The American slice is chosen for melt behavior, softening against the residual heat into a thin binding layer that ties the fillet to the vegetables. The result is a fuller, more cushioned sandwich than the original, with the crunch of the crust now competing against lettuce and the salt of the fillet now mediated by tomato and cheese rather than standing alone with two pickles. It is a more conventional fast-food chicken sandwich by design, which is exactly what makes it a useful contrast to the stripped build it descends from.
The other codified members of this cluster are the minimal original and the cayenne-brined spicy, and the spicy build can itself be ordered in deluxe form. Each of those deserves its own article rather than being crowded in here.