#1 and #2 Diesel Fuel are the primary fuel types for mobile and fixed diesel engine applications.
When buying fuel, #1 is often labeled at the pump as "Premium Diesel" or with a Cetane number of 44 or 45. It is thinner and a better choice in the winter.
#2 Diesel Fuel is thicker. Since it is thicker, it has more lubricating properties. Diesel #2 Fuel will gell easier in cold weather. This makes starting harder. It can also cause rough-running.
#2 Diesel is often labeled at the pump with a Cetane Number of 40
Home Heating Oil is NOT #2 Diesel oil. It is very close. It may have the same in ignition quality and lubricating ability only. Refiners do not intend Home Heating Oil to be used in an internal combustion engine. Fuel that is intended to be burned in your furnace, may not have the smoke suppressants, ignition accelerators and biocides to kill fungi and bacteria that is generally are present in the Diesel Fuel at the pump. The ones that Automotive vehicles use.
If you use #2 heating oil in your generator, you are at risk of causing serious damage. Using #2 home heating oil will void any manufactures warranty. Some of the first problems users encounter is damaged fuel pumps, fuel injectors and engine glazing.
The heating oil companies want you to buy their fuel and do not care about your engine. They will say it is the same #2 diesel fuel with red dye added to it. All they want to do is sell you fuel. If heating oil was safe for compression engines, the fuel compaies would advertise this. They do not. Many articles can be found on this topic. Not one article can be found from a fuel company telling you any differently.
Kerosene is added to diesel fuel by some suppliers, though in small quantities. Kerosene has virtually no lubrication qualities.
Kerosene is routinely added to home heating oil, in large quantities. The furnace does not know, or care. The furnace oil pump does not have the same clearances (they are more crude, greater clearances, lower pressure...) and the kerosene will not hurt them. Most will and often do run on straight kerosene. If the oil tank is outside, the mix will be either 50/50 or straight kerosene. Kerosene does not have the same heat values. You will not get the same amount of power from a gallon of kerosene, as from heating oil, or diesel fuel.
Your engine needs the fuel additives that home heating oil is missing. If you are using home heating oil, it is a sure way to cut the life of your fuel injector pump, fuel injectors and the rest of your engine.
If something fails due to fuel quality, it is not a manufacturing defect and will not be covered under any warranty.