The questioner (Ben) suggests this as the distinction between the two:
To me, you remake a singular film, and you reboot a franchise. "Stargate" can be rebooted because the TV series has continuity, and you can reboot or reset the continuity like a computer. There's no continuity to "Cliffhanger," though; it was a one-shot story. So it's a remake of "Cliffhanger," not a reboot.To me (as well as to John and Craig) this makes total sense. And yet, as Ben points out, the entertainment industry rarely makes this distinction in practice. Virtually any time you read in Variety or Deadline about a new version of an existing property, the term being used is "reboot" (or "re-imagining," which wasn't mentioned on the podcast but is also commonplace) by either the publication or the studio or both.
For one thing, there's the fact that Hollywood is, always has been, and always will be addicted to buzzwords. The moment a word or phrase becomes associated with something cool or popular or innovative, everyone instantly wants to use it to refer to everything, regardless of whether it actually fits. (I guarantee you that right this second, an executive somewhere is using the phrase "killer third act" to describe a macchiato.) Reboots have been having their moment ever since the mid-aughts, when Batman Begins and Casino Royale kicked off the trend (followed by Star Trek a few years later). Remakes just haven't enjoyed the same cachet; some have been successful (the Steve Martin Pink Panther) and some have been well-reviewed (the Denzel Washington Manchurian Candidate) but I can't think of any that have really lit the place up. Studios want to use the term associated with big hits, so they're apt to say "reboot" no matter what.
But while I think optics is a big part of this issue (as it is with most issues in Hollywood), I think there's more to it. I think the word "reboot" genuinely speaks to what studios hope and believe is possible with the films they're making.
The original Cliffhanger was a huge hit, taking in over $250 million worldwide (in 1993 dollars), and Stallone was still at or near his peak of stardom, but there was never a Cliffhanger 2. (In fact, of the top ten grossing films of 1993, the only one that was sequel-ized was Jurassic Park.) Here, twenty-one years later, such a situation is pretty much unthinkable; a studio president could easily be fired for declining to greenlight a sequel to one of the biggest movies of the year. And you can bet that the new version of Cliffhanger will be written with an eye toward making it a franchise, and that its stars will be contracted for at least three films. That's just the way things work now. (Pretty much the only studio movies that aren't designed with sequels in mind are Oscar-bait films, and there are even exceptions to that rule.) So, when Cliffhanger is referred to as a reboot -- even though it only ever existed as a standalone film that wasn't part of a larger mythology -- it's not an accident, and it's not just chronic buzzword-ism.
The one time the word "remake" is still useful is when a foreign-language film garners so much buzz from festivals and the Internet that an American studio decides that they need to produce their own version of it (Let Me In, for example). And in these cases, the studio wants to indicate that the movie will hew pretty closely to its source, except that it'll be in English with actors we all recognize. They're not trying to reinvent the wheel; they're just trying to sweep up all the money that was left on the table due to subtitle-phobia (and the fact that foreign films are rarely screened outside of major cities).