Both sentences are grammatically correct. Fuel (non countable) is a substance used to provide energy to do useful work, usually by burning; "petrol" ("gasoline" in US English) is one kind of fuel. A fuel (countable) is one type of such a substance. Wood and coal can be fuels for fires, e.g. in stoves or furnaces. Gunpowder can be used a a fuel for rockets. Motor vehicles that are not solely propelled by electric power can use a number of fuels: diesel oil, hydrogen gas, liquid petroleum gas (LPG), butane gas, propane gas, and others.
The first sentence would be used if the speaker meant to discuss taxing all kinds of fuel for private cars, and the second would be used if only petrol (or "gasoline") was to be taxed.
"Collecting more taxes" is unclear; it could mean "introducing new taxes", or "collecting existing taxes more efficiently or rigorously". If the desire is to convey the idea of increasing tax revenue, then "more tax" is better.
Also, 'raising' has a special meaning in relation to taxes - taxes are used to raise (produce) money for governments; to avoid this ambiguity, use 'increase' instead.