Everyday household and construction debris is fine. The limits come from New Jersey's waste rules and from the county landfill that weighs your load.
New Jersey has required source separation since the 1980s. The state recycling law makes every county name at least three recyclable materials, plus leaves, that must be kept out of the trash, and each town writes that into its own rules. In practice that means cardboard, metal, and clean wood are worth setting aside rather than burying in the load.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos never belong in a standard container. Camden's older housing stock can hold asbestos in pipe wrap, floor tile, and siding, so have suspect material tested before a crew starts tearing it out.
Tires, refrigerant appliances, batteries, and electronics all need separate handling. Mention them to your account manager when you book, and they will arrange the right route for each one.