Our heating oil deliveries are marked “ dyed diesel fuel” and after some pressing, a supplier adnitted that they are in fact the same product. My undersatnding is that the reason they add dye to home heating oil is so that if it is put in on road vehicles it can easily be detected. People I lnow have run home heating oil in diesel engines for years without incident. One farmer Got caught at market & was fined pretty heavy, he told me he had been running it for years though.
Kerosene is a slightly more refined product, but can also be burned in your diesel, or oil burner. Not sure of the long term ramifications of that though.
I often hear of people with above ground outdoor tanks adding K-1 in the winter to help combat the molasses they experinece in the cold weather
C