Without trying to bore anyone with to much technical stuff here; but we're comparing Apples and Oranges.
The current trend toward development of aero-diesel engines is to provide access to one of the most common fuel sources around (especially at airports) - Jet Fuel.
Although Diesel is the colloquial term for any Diesel fuel there are a number of particular and subtle differences between the refined varieties of diesel fuel and their applications.
Jet Fuel (Jet A-1, A-50 , etc) is identical to what refiners term #1 Diesel, or #1 Stove Oil. In order to define and qualify a fuel as Jet Fuel, the product needs to conform to a delivery quality control and batching system. The final bulk delivery would be filtered through an anhydrous clay filter, to ensure that all refining and transportation surfactants are removed from the product. Certain vendors will add additives (anti-icers, etc) to the fuel to produce their special brew.
All the bulk product delivered from the refiner conforms to the Jet-A standard and may be removed and downgraded from the QC system and delivered in it's various commercial identifications (#1 diesel, #1 Stove, etc.), as required by the consumer.
#2 Diesel, the automotive brand is an entirely different product, designed for automotive internal combustion engines. Significantly, it has added oil and sulphur in order to improve lubrication. It is NOT interchangeable with #1 diesel - it is a wholly different product and is (generally) not suited for use in Jet engines.
(You can blend your own #2 by adding oil to #1 diesel.)
The flight manuals for any of these aviation applications will clearly define the list of approved fuels, and in some cases the list will actually include non-aviation fuels including #1 Diesel, Arctic Diesel or some other variant of the same product. Many of these alternate fuels include the requirement that the alternate fuel be refined to ASTM-1655, so we come back to the beginning, and the refining cycle of all the original bulk fuel that starts life out as Jet-Fuel!
If you are still awake at the end of all this, I hope it answered a part of your question.
