"Jet A is also JP4." This is not correct. The industry equivalent of JP4 is JET B. Both JET A and JET A1 are both kerosnene base fuels.
"We now use JP8 because it has a higher flash point and it works better in military deisel trucks." The main reason for the military switching to JP8/JET A1 was due to the waxing problems that the Abrams tanks were having once deployed in German in the early 1980s. To remedy this, they had to blend in 50% kerosene or JP8/JP5 which then became a logistical problem. Further testing revealed that diesel engines as well as turbine engines could perform acceptably on the kerosene based jet fuels. Then the switch was made.
"JP4 works in deisel trucks but it may burn too hot for some." Wrong, as JP4 typically does not have sufficiently high cetane quality, is too volatile, and therefore cannot be used in certain diesel engines. It worked fine in multifuel engines, but the military phased these out a long time ago.
"I understand JP8 is more like Jet B." Wrong, JP8 is very similar to JET A1 except that it dos not contain the three mandatory additives that convert JET A1 to JP8.