i think officially a chicago style dog would be classified by both the dog itself (Vienna Beef) and the accoutrements...if I remember correctly, include Mustard, Onion, Relish, sliced tomatoes, sport peppers, a pickle, and celery salt all in a slightly steamed poppy bun.
unfortunately most of the time I had these while completely blitzed and getting cursed at by the Wiener Circle workers (as is their custom) at 4am, so the details might be a touch off.