This subject has been discussed ad nausium, but usually the other way, using fuel oil in diesel engines. To recap, I contacted a number of oil companies regarding this, and according to what they say -- it will vary by locality. In some areas, mostly rural where there is a low density of buildings, the furnace oil "may" be identical to diesel fuel, in populated areas, where they can afford separate supply lines, there is a major difference between diesel and heating oil. Mostly the diesel is high quality oil with additives to ensure that the engine will run properly. In these areas the heating oil can be any old crap (my words) that meets the minimum specifications and will burn in a furnace.
The summary, diesel oil will work fine in your oil furnace, but in most cases it will cost more because it is a premium product. In your case it may be cheaper.