Jet-A, Jet A-1, & JP-8 are all about the same except for the additives for anti-icing & anti-corrosion. JP-5 has a higher density for Navy ops and about the same additives. JP-4 & Jet-B are about 40-60% Naptha with kerosene since it has a lower and wider distillation temperature and is lower density (~6.5 Lbs/gal) than JP-8 (~6.8 lbs/gal). JP-4 also has the best anti-icing package. K-1 doesn't have any of the additives except maybe red dye and is a little more pure than bulk jet fuel. K-2 has a higher sulfur content more like jet fuel (Jet A). This is all out there online. I spent hours looking it up a couple years ago but don't have the URL's anymore.

I'd use JP-8 in my P-80. Are you getting it as waste fuel or fresh from a government installation??