i'm sure it can, i'm just passing along what version i was taught and how i see the differences between the two styles i eat the most often. the one i'm talking about is from the Santa Fe and Pecos NM area and i'm not sure how far it goes back but quite a long time as my sister's ex-husband's Mom has gotta be in her 90s.
how it was used was for pretty much any way you wanted to, there was no requirement for beans, or even the kind of meat, whatever was available and sometimes made without meat at all. never tomatoes. tomatoes would be used in other things and the chili sauce added, but never tomatoes in the chili itself. also never fresh chilis. fresh chilis were instead used in season and the dish was specificly called Green Chili Stew and in that area the Hatch Green Chilis are still a big event. my SIL has a box shipped to her each year so my brother can roast them up and then they put them in the freezer. some years hotter than others. always good.