If all uses of a fossil fuel produces the exact same carbon output, but my understanding is that this is almost never the case.
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).
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?
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.
The stuff that is turned into lubricating oils, plastics, etc... will keep most of the carbon contained.