There are some significant differences between diesel, kerosene and fuel oil. Most have to do with lubricity which is life or death to a diesel engine, and some to do with soot control that affects the combustion process.

As for the cost difference with gasoline, again many factors but ULSD (Ultra Low Sulphur Diesel) is the cause for the most recent disparity. Like lead in leaded gasoline provided lubrication for engine valves the sulphur in diesel is used to enhance overall lubrication. Remember, when Rudolph Diesel invented the "compression engine" it was designed to run on peanut oil. Vegetable oil has far better lubricity than petroleum products so the sulphur was added to create a fuel for the diesel engine, but now that same sulphur is a nasty source of pollution.

Keep in mind also that there's more energy in a given volume of diesel fuel than gasoline, hence the better mileage most diesel vehicles achieve. Right now my 4000 pound VX gets around 17MPG average from $2.34 a gallon gasoline, where my 4000 pound diesel Mercedes gets around 34MPG average from $2.89 a gallon diesel. Twice the mileage from a $.55 price difference? I'd buy that all day long!