I have no trouble in defining/describing the dish... (which is a simply unadorned Braised Beef, more "Anglo" than Mexican)

Traditional Version close to that sold by San Antonio's "Chili Queens" in the Mid19th Century

Ancho and other dried chiles, optimally soaked and pulped. "Ground" chiles may be substituted, and even some "Chili Powders" Amount and varieties of chiles adjusted for desired "heat", but original "Chili" seems to have been reasonably mild but with hot chiles on the side for garnish.

Cheap cuts of beef cut into small cubes.

Garlic
Cumin (brought from the Canary Islands by original San Antonians?)
Salt
Chopped onions
Water or beef stock
Masa to thicken

Assembly varies.
Tomatoes are forbidden by Papal Interdict, and the addition of Ketchup is a 3rd degree felony.

Frijoles, Pinto, Anasazi, Salvadorean (but never Kidney or Black) must be served separately.

Leave out most/all of the beef except for some suet and it's "Red Chili Gravy", TexMex enchilada sauce.

Acceptable "Anglo" garnishes include chopped raw onions, grated Cheddar, Tortilla Chips/"Tostados" or the ubiquitous "Fritos", the base for cultural icon "Frito Pie" served "in the sack". Warm corn tortillas work well when a spoon is not available

All else is extraneous, by custom, tradition and precedent to be avoided. Green Chili is from New Mexico. "White Chili"? Less said, best said!