A cheesesteak witout is the same sandwich as a cheesesteak wit with one component subtracted, and the subtraction is the entire point. In Philadelphia the order is compressed into a single spoken word at the window, and witout means without the fried onions that otherwise go down on the griddle before the meat. Calling it a distinct sandwich at all is a Philadelphia habit: the build is identical, the cheese decision is identical, and the only difference is that the sweet, soft layer the onions provide is gone, which changes the whole balance of the thing.
What that subtraction does is structural as much as it is about taste. On a cheesesteak with onions, the onions are cooked down on the same steel as the ribeye until they go limp and sweet, and they fold into the chopped meat as a moisture-rich counter to the fat. Take them out and the sandwich becomes a tighter argument between just two elements: thin-sliced ribeye seared and chopped fast on the flat-top so it stays pliable, and cheese melted into it on the steel rather than laid on after. Cheez Whiz, sliced provolone, or American is still the standing choice, and witout sharpens it, because there is no third sweetness mediating between the cheese and the beef. The roll matters more here too. With less moisture going into the pile, the long Philadelphia roll, tender inside and structured enough at the crust to carry a heavy fused filling, has an easier job holding together, and the eater tastes the bread more clearly.
The ordering grammar is the real subject. Wit and witout refer only to onions, and they combine with the cheese call into a terse compound: whiz wit, provolone witout, American witout. Each permutation is the same method with a single variable flipped, which is why the window can run the whole menu off four words. The pizza steak, the pepper steak built with long hots, and the mushroom version are nearby builds that change a different variable on the same griddle, and each of those deserves its own article rather than being crowded in here.