Are there more impurities in home heating oil?
I'm in New England, and like many US states, we have a 25c/gallon tax on '#2 Road Diesel' (tax paid, no dye added), this is always Ultra-Low Sulfur Diesel (ULSD). Generally fuel sold for use in cars is only about 10-15% more expensive than fuel sold for use in a furnace, and most of that is highway tax, not extra distillation at the source.
For Delivery, you can can specify either 'Home Heating Oil" or "Off-Road Diesel". Both are #2 Diesel and contain dye (indicating no road tax was paid), and in most US states, both are at least Low Sulfur, but several states now mandate ULSD for heating oil. There is more margin for variation in the grade of oil sold as heating oil than for off-road diesel, but usually they come out of the same tank & truck. Off-Road Diesel is used for construction equipment, generators, etc. In the winter, when delivering off-road diesel, they might add kerosene and/or additional anti-gel treatment, only because home heating oil is usually stored underground or in a basement while construction equipment and storage tanks are more exposed to the elements.