Kerosene is as close as you can come. Distillate, also called "power fuel", was between kerosene & diesel in the old refining method, basically a by-product, so it was cheap, like 3c/gal. in the 30's. When the catalytic cracking process came about, more of the crude was able to be made into gasoline, which there was more demand for, so distillate disappeared. Gas or Diesel was more trouble-free to burn anyway. They had to be started & warmed up on gas. Kerosene can be burned in the old distillate engines, but it's no longer cheap. Diesel can be used if it's cut with some gasoline, but again, not cheap any more...
The old-timers said a tractor like a John Deere D would really pull when you got it hot, switched to distillate, & turned on the water injection to kill the knock...
You are right to have a bit of confusion about distillate and from what I've learned and experienced there are several different names and a couple of different sources.
Back in the 1930's some of the farmers on the Carrisa Plain (between San Luis Obispo and Bakersfield) would come down off the Tembloers to Taft and McKittrick with a tank and buckets and dip free fuel from the oil well cellars. They called it " Casing Head Gas", "Drip Gas" or Distillate. It was free fuel for the Cat 60 but a rather dangerous endeavor because of the H2S.
In North Dakota, We called it distillate and or drip gas.
The oil in the Bakken is a very light crude and has a gravity between 42 and 48. I've heard that it refines out on average at 60% diesel, 30% gasoline 5% paraffin and 5% is used for the refining process. When we would gauge a tank you would notice a 1/4" to 3/4" of gas standing on top of the oil.
There is an abundance of wet natural gas in the Bakken wells and it could come out of the ground very hot. 130 to 180 degrees. At a lot of locations, the gas had to be cooled before it could be shipped down the pipe lines as they were made of a durable PVC. The cooling process would yield a goodly quantity of drip gas or distillate.
There was no official market for this product but a some did find a home for it blending it with some of the heavy crude that came from the wells that were drilled in the 50s and 80s before fracking.
Words and their meanings some times interchange with the passage of time so the preceding is my perspective on the definitions.
Casey
Well stated Casey.
Old guys used to tell me Casing Head Gas was good for washing clothes because when they were hung to dry, they would "freeze dry".
Distillate does make good power but the issue of knocking usually meant the engines have lower combustion ratios with retarded timing than Gasoline.