Chili just a knock off mole. Which I mean to make one of these days. I've been put off by the nuts, because one daughter is allergic.
Chili and chile are two entirely different things, which is why I made the distinction.
Chili is a dish of meat, chile peppers, and spices.
Chile is a sauce or gravy made from chile peppers, and spices, and in some cases as you say, nuts and other additives. Mole is one type of chile sauce, but there are dozens more throughout Mexico, all regionally specific. And of course New Mexico and Texas have their own versions of chile gravy as well.
I've made mole and many other Mexican chile sauces before, I really enjoy experimenting with the different spices and flavor profiles.
I've spent a lot of time in the interior of Mexico and I don't think I've ever actually seen Texas/American style chili, anywhere. They have tons of dishes consisting of various braised/stewed proteins in with chile peppers and spices, but nothing that matches the consistency and flavor profile of what we call chili.