They quite often are, but not as much as is necessary. Oil tends to be taxed at refinement, but there's no such stage for coal.

If all uses of a fossil fuel produces the exact same carbon output, but my understanding is that this is almost never the case.

Burning the same fuel is always going to produce the same amount of CO2. Here are the amounts, for various fuels:

https://www.eia.gov/environment/emissions/co2_vol_mass.php

You might get more or less usable energy out of it depending on your efficiency, but if you're less efficient you'll have to burn more fuel (hence paying more tax, directly or as part of the price of fuel if it's taxed at the source).

But fuel is not the only use for those resources.

But isn't it the case that

A) petroleum products are used for other purposes?

B) carbon capturing is used to various levels of effectiveness?

C) there can be different levels of partial combustion?

A) We could address this by charging at the refinery for fuel products, rather than at the oil well for crude.

B) I definitely think carbon capture should earn credits in any carbon pricing system.

C) That's just another kind of inefficiency. Same comment applies as above.

All of the fuel that is burned should release roughly the same amount of carbon.

The stuff that is turned into lubricating oils, plastics, etc... will keep most of the carbon contained.

… but will nonetheless pollute the environment in differently harmful ways.

Yes but (for instance) some people who are 100% on board with reducing CO2 emissions to prevent global warming have different views about using fertilizer or plastics.

What about carbon capture?

Mostly doesn't exist.

But if you did that then drivers would have to pay their fair share instead of pretending like bitcoin actually matters.

Yes, but I think Earth's general voting population is too short-sighted to support something like that.