You are correct. Being so close to the Mexican border, I can say tacos are mainly a soft corn shell filled with the meats you mentioned + adobada = marinaded pork, tripas = tripe, lengua = tongue, cabeza = brain & the main ones I see -- carne asada & carnitas (grilled beef & shredded pork) topped with pico de gallo or just chopped onions, cilantro & usually a spicy sauce on top. Trompo is actually the vertical rotisserie or "spit" the meats are cooked on.
And they are actually really tasty (minus the meats from other places of the animal). San Diego has been replicating the style with a chain called "Tacos El Gordo" and it has really taken off, with one in even Las Vegas now. Anyways, back to your regularly scheduled programming of Elfie trolling and Tibs riding his coattails.