Fuel is an all-encompassing and imprecise term for substances that can store energy easily released through a simple chemical reaction, typically combustion.
Oil is a family of non-polar hydrocarbon substances which can be used as a feedstock product to make fuel, among other things.
Crude oil is specifically oil from underground fossil carbon sources, which is often refined into various products, including fuels like gasoline/petrol or diesel.
Natural gas is a term for methane-rich hydrocarbon gases typically associated with crude oil deposits, and which can be used for fuel.
Gas either is a term for natural gas, or specifically for gasoline fuel, depending on context.
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