Most of what a remodel or a cleanout produces can go straight in. The limits come from Alabama's disposal rules and from the county transfer station.
The Alabama Department of Environmental Management treats household trash, furniture, roofing material, other construction debris, and scrap tires as regulated waste, which means it belongs in a permitted landfill and nowhere else. Burning it or dumping it on a back lot is not allowed. That is the reason a container matters on a rural property, where a burn pile can look like the easy answer.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos stay out of a standard container. So do car batteries and anything holding Freon unless a certified technician pulls the refrigerant first.
Tires are their own case. The state limits how many scrap tires can sit on a property and says they should be kept out of the weather, so set them aside and mention them when you book rather than burying them in a load.
The state does treat clean, unpainted concrete and brick, along with stumps, limbs, and leaves, as unregulated, which is why keeping those in a separate load is often the cheaper route. Ask your account manager if an item has you guessing.