It's a pretty complex thing, but here goes:
RV appliances (refrigerator, stove), grills, and the like all operate on gaseous propane. And so do motors on forklifts, LPG-cars, etc.
So what's the difference? The difference is essentially
the point at which the conversion takes place from liquid to gaseous state. In your RV, the conversion to gaseous state takes place right inside the propane cylinder. By contrast, in the forklift (and like motors) the propane is delivered under pressure as a liquid from the tank to the motor, at which point the conversion to gaseous state takes place in (or very close to) the motor's intake sytem. (Of course, there's lots and lots of complex technology involved, and these will make a difference in the end, too.)
Bottom line: No, you can't just use a tank from an LPG-powered motor in the RV or your grill.
Second bottom line: If you've followed so far, you'll also recognize the danger of attempting to use an RV bottle in its incorrect position: A horizontal cylinder must be horizontal, and a vertical bottle must be vertical. Failure to do this will permit liquid propane into your RVs propane vapor distribution system, a very, very bad idea.
In fact, it's kind of hard to locate good info on this stuff, but one place to look is at the Wikipedia under the term "autogas."