The American gyro is defined by the cone, not the cut. Where a Greek gyro stacks marinated slices on the spit, the American street version runs on a manufactured loaf: ground lamb and beef bound with seasoning and pressed into a dense, uniform cylinder, frozen, then mounted on the vertical rotisserie to roast and be shaved as it turns. That formed cone is the whole reason the American build is consistent from one storefront to the next. It is engineered to give the same crisp-edged, even shave at the bottom of the cone as at the top, which a hand-stacked spit cannot promise, and that uniformity is the sandwich's defining quality.
The craft is in the rotisserie and the wrap. The cone turns against a vertical flame so its outer face crisps and renders while the interior stays moist, and it is shaved thin from that crisped face to order, so every portion is a mix of browned edge and tender inside rather than a uniform slab. The flatbread is a soft, pliable pita warmed on the same grill so it folds around a loose, hot, wet filling without cracking or going stiff. Tomato and raw onion are the cool, acidic crunch against the rich shaved meat, and the tzatziki, a thick yogurt and cucumber sauce, is structural as much as flavor: it binds the shave to the bread and keeps the wrap from being only meat. The pita is folded, not rolled flat, into a cone of its own that holds the filling at one end so it can be eaten in hand on the move. This is a griddle-and-rotisserie street build, the cone roasting continuously through service and shaved down across hours.
The variations move with the meat and the wrap. A chicken cone in place of the lamb and beef, a platter that abandons the bread for rice and salad, a build that swaps tzatziki for a hot sauce. The wider folded-flatbread shelf, the shawarma, the döner, the taco and burrito, runs the same containment logic with different fillings and sauces. Those deserve their own articles rather than being crowded in here.