Here is some info from a company that installs diesel generators:
Off road Diesel #2 and Home Heating Oil / Fuel Oil # 2 differ only in the tax applied at the time of sale.
Both are dyed red. They differ from standard Road Diesel #2 in that road tax has been applied, no red dye has been added, and there is a specification regarding ash and/or sulphur content. In extremely cold climates, Standard Road Diesel #2 may be blended with Diesel #1 or Kerosene K-1 to assist with gelling problems resulting from the cold weather. Similar blending may occur on home heating oil / fuel oil based on your geographic region, anticipated temperatures, and overall climate.
Home Heating Oil / Fuel Oil #4 and Home Heating Oil / Fuel Oil #6 have a higher BTU content. This is normally accomplished by adding much heavier petroleum oil distillate similar to normal automotive motor oil to the formulation. This allows a furnace to burn less fuel, for each BTU of heat produced, as well as often times reducing the cost per gallon of fuel. These types of Home Heating Oil / Fuel Oil should NOT be used in a Diesel Fueled Engine or Generator.