Biodiesel basically is made from adding methoxide (methanol and either KOH or NaOH) to vegatable oil and heating it to 125 degrees. the resulting chemical reaction produces Biodiesel and Glycerol.
Biodiesel can be added directly to the fuel tank without modification, while running veg oil requires a two tank fuel system where in a nutshell you start the engine on diesel, switch it over to vegatable oil when the engine warms up, and switch it back once you are about to shut it off.