Maybe this is implied in my earlier posts, but, in the interest of clarity:
At least from how I experienced it, the pre-history of minimal was tech-house in the absolute broadest sense of the phrase, encompassing all of the different styles I mentioned below. At this point, there was still an interest in maintaining the more experimental spirit of the history of techno and house by finding a place outside of hard techno and big-room house, which was essentially US vocal garage.
Prog always seemed to me like an attempt at refining out those experiments, whereas this occurred over time with minimal, and almost accidentally, which is why the original practitioners were the first to abandon it.
Minimal is like a language formed solely from the specialized terminology and unjustly antiquated phrases of other language. When it became its own language, however, new words became outliers as the vocabulary went through the same narrowing that had allowed minimal to exist in the first place.
And the last thought:
Minimal likes acid, liked electro, liked rave, liked early trance. Prog didn't (the TB-303 was used, but never with the intensity of acid house or acid techno). They started at different places, in different mental spaces, and ended up similar at the end.
And now I have to stop this while I can.