Jet-A is a relatively high sulfur fuel, diesel is low sulfur and EPA requirements are getting more stringent about sulfur in diesel every year. After all, we are now in the Ultra-Low Sulfur diesel era. Using Jet-A in your truck will be highly frowned on by your EPA inspector and could lead to fines.
Jet-A is “dry.” Diesel is made in such a way, or additives are mixed in, to lubricate the injector system of a diesel engine.
Jet-A is closer to kerosene and Diesel #1. Most modern diesel engines specify Diesel #2.
The viscosity specifications for the two fuels is different. Jet-A and Diesel #1 tend towards lower viscosities than Diesel #2. Lower lubricity is likely as the viscosity decreases. This may not cause catastrophic instant damage, but it may cause long-term wear of pumps, injectors, etc.
Cetane number. Diesel #2 is manufactured with a required cetane number. ASTM D975 specifies a minimum of 40. Most Diesel #2 in the U.S. is 42-45. The ASTM specification for Jet-A, ASTM D1655, has NO minimum cetane rating, because cetane pertains to compression ignition engines, and has no meaning in turbine engines. Using a fuel with too low a cetane number in a diesel engine will just result in a rough-running or not running at all engine. This is why Exxon required pilots of Diamond aircraft with Thielert diesel engines to sign a liability release to fill up with Jet-A at Exxon airport supplier