Does BTU output change with the fuel type?

Yup. Fuel types are rated by heat per cubic foot. Propane is rated at 2516 BTUs per cubic foot, whereas Natural Gas is rated at 1030 BTUs per cubic foot. You can maximize your BTUs by using a larger burner. On the flip side, to reach a lower BTU using a higher heat per cubic foot Fuel type, a smaller burner may be used.