Wikipedia distinguishes between waste vegetable oil (old chip fat), straight vegetable oil (new chip fat) and biodiesel, which is vegetable oil modified especially for replacing diesel.
Most cooking oil is too viscose to be used as a direct replacement. One way to reduce the viscosity is to heat it. If you start an engine with normal diesel and use the heat generated to warm your vegetable oil, then switch to the vegetable oil, and switch back just before you turn off the engine, you can use vegetable oil without ruining your engine.
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