Vegetable oil is renewable, fossil fuel is not.

Vegetable Oil Fuel Conversion

Yes. Vegetable oils are used to make bio diesel, which can be used like conventional diesel.

Vegetable oils are also used to make biodiesel, which can be used like conventional diesel. Some vegetable oil blends are used in unmodified vehicles but straight vegetable oil, also known as pure plant oil, needs specially prepared vehicles which have a method of heating the oil to reduce its viscosity. The vegetable oil economy is growing and the availability of biodiesel around the world is increasing.

The NNFCC estimate that the total net greenhouse gas savings when using vegetable oils in place of fossil fuel-based alternatives for fuel production, range from 18 to 100%.

source: Wikipedia

Biodiesel fuel can be made out of many organic compounds. Vegetable oil and corn oil are two things that can be used.

Diesel engines can be operated with 'biofuel' with the proper adjustments.