I make chili, and I also make chili with beans. Texas Red is my favorite, actually just made another batch. Here's how I make mine.
First I make the chili sauce. I like to use 7 different types of dried chilis, adjusting the heat depending on whether or not I have little mouths or yankees to feed. I use chili ancho, chili guajillo, chili pasilla, chili arbol, chili morita, chipotle chili, & chili tepins. Gut the chilis, and then toast them in a skillet over medium heat (don't burn them). This makes a difference.
I quarter a red onion and throw it in a pot with 6-8 large cloves of garlic, add enough water to cover and drop in two cubes of Knorr chicken bouillon. Boil for 5 minutes, then add the toasted chilis and boil for 5 more minutes. Keep covered, turn off the heat, and let sit for 20-30 minutes. Then add all into a blender with just enough of the liquid to cover, add 1 tsp of cumin, 1 tsp hot Spanish paprika, and puree. Then I run the sauce through a screen to remove all of the pulp - set aside.
I trim my meat well and cube it up into about 1" pieces. Salt & pepper the meat or use fajita seasoning, I prefer fajita seasoning. Heat my cast iron pot up to med-high heat and drop meat in dry, I want it to stick to the bottom (don't overcrowd the pot). Once meat is browned set aside. Then I reduce my heat to med-low and drop in one diced red onion and some butter (real butter only). Sautee them onions down until they're real dark & caramelized, making sure you remove all of the goodness from the bottom of the pot while stirring. When the onions are ready, I remove almost all of the butter (leaving maybe a teaspoon), then I drop my meat back in/pour in the chili sauce/give it a good stir. Cover and reduce heat a little so to simmer about 2 hours or so, until meat is fork tender and the gravy is the consistency that you want. Remember the meat will make a little water on it's own while cooking, so don't go crazy adding water at the beginning. Taste for salt at the end.
I use venison, pork, beef, whatever. I like to make a batch of chili sauce ahead of time and take to camp with me. Pull some meat from a fresh killed deer or pig and make a pot of chili right there. For a little extra heat and flavor, crumble a few dried chili tepins over the top.
I like to serve with either cornbread, biscuits, toasted corn tortillas, or over rice.
If you want to make chili soup you can use ground meat and add tomato paste/tomato sauce/diced tomatoes/ and beans, just don't call it Texas Chili.