The defining move of the New Jersey Texas weiner is that the hot dog is deep-fried, not steamed or griddled, and the name has nothing to do with Texas. This is the Greek-American diner tradition that runs across New Jersey, and it starts by dropping a natural-casing frankfurter into hot fat until the skin blisters and tightens into a hard snap. That fried exterior is the structural choice the whole sandwich is built on: it gives a deeply seasoned, wet build a component with real crunch and a casing that resists going soft under a ladle of chili, which a boiled dog could never do.
The craft is in the fry and the fixed dressing order. The dog is fried until the casing crackles and bows slightly, then set in a soft, plain bun whose only job is to absorb without competing. The chili is a fine, spiced, loose meat sauce rather than a chunky bean chili, cooked smooth enough to coat the fried dog and cling along its length. The dress is a set sequence, summarized at the counter as all the way: a line of yellow mustard down the bun, the fried dog, the spiced meat sauce over it, and chopped raw onion scattered on top. The order matters structurally as much as for flavor, with the mustard placed to read through the sauce and the onion last so its cold crunch sits against the soft warm pile. Diners build several at once on the forearm and dress them in one motion, which is why the build is codified to the gesture.
The variations are mostly which diner's chili and how it is ordered. All the way is the standard; dropping the onion, adding cheese, or doubling the dog are the common moves inside the same fried-dog build. This New Jersey deep-fried reading is distinct from the Scranton-area Texas hot weiner, which uses a non-fried dog and a different all-meat sauce, and from the Midwestern coney that shares the spiced-sauce idea but not the fryer. Each of those deserves its own article rather than being crowded in here.