Can anyone explain the difference? Do some people like one but not the other? How does this happen?

They actually have similar goals musically speaking, and I think artists like Mike Oldfield, Brian Eno, King Crimson etc all released music that is prototypical Post-Rock to my ears. Some regard Post-Rock as an offshoot of Prog Rock, for example Prog Archives lists it as one of Prog's subgenres, a viewpoint I have a lot of sympathy for given the influence of some 70s Prog bands had on the genre.

Really the best way I can describe any contrast is this. Prog Rock is the use of non-rock instruments in a rock setting, albeit rock that's fused with other genres. Post-Rock relies much more heavily on traditional rock instruments to create sounds and structures not usually associated with Rock. Also the variation in tempo and time signature found within a lot of Prog Rock isn't nearly as common in Post-Rock. There's also less emphasis on virtuoso musicianship in Post-Rock. Prog bands of today take more influence from 70s Prog and Hard Rock, compared to the Indie and Alt-Rock influence on Post-Rock.

This is an excellent question, one I shall ponder further over the next few days. It might be worth bringing it up in the general Music Discussion section, as there are people there who could perhaps give a more fuller answer, or at least more input.

Okay I'll bring it up in the general Music Discussion.