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Usually, at least from what I've seen around here, it's just a difference in the Cetane rating. Texaco stations around here carry "premium" diesel (45 Cetane) and the rest pretty much carry 40 Cetane. The cost of 45 is usually about 10-15 cents higher than 40. I usually use Stanadyne with the 40 Cetane and it seems about the same as 45. When it's really really cold out, it also seems like the higher cetane fuel will help the truck start better.
Premium diesel can have a higher cetane rating, but it does not have to.
Refiners can put in better additive packages, more additives, or a higher cetane number and have the right to call the diesel "premium".
Cetane can vary from barrel of oil to barrel of oil. That is why most refiners will only say the "minimum" cetane number, usually around 40, but the cetane can vary from lot to lot from the low 40's to the upper 40's.
Amoco sells a "premium" diesel that they claim has a minimum cetane rating of 50.