The distinction - if you want to draw it - is usually on how hard they break it.
Mass Effect is actually plausible. It’s not bloody likely, but it at least attempts to use existing physics to explain itself (specifically, it attributes observed dark energy to their magical material that changes the apparent mass of stuff when you pass current through it).
Battlestar Galactica (the new one) didn’t try very hard - it’s just a thing that spins and then you push a button and you’re in a different place than where you were before, but because it’s more of a wormhole generator and less of an FTL device (jumps, rather than transit time), it’s still at least at a point where Michio Kaku would tell you that it could theoretically happen, maybe.
Star Trek used to be plausible, before we conclusively and firmly disproved any kind of warp field theory. Essentially, they got around the FTL problem by submitting that the object itself was not moving faster than light, but space in front of and behind the object was being expanded or contracted in such a way as to affect faster than light travel through conventional space. They actually had physics dudes worry about this for them at the time.
The Gap Cycle is somewhere between Battlestar and Trek and serves to exemplify most FTL in fiction these days, which posits the existence of a “sub-space layer” where you can draw a straighter line than straight in normal Euclidian geometry, so you can go faster than fast. This is almost definitely not the case.
Hyperspace, from Star Wars, is a loosely defined catch-all for “a thing what goes all fast.” It has transit time, like Warp Theory, and it moves through conventional space, as evidenced by the fact that gravity wells and the artificial generation thereof are very real concerns (though I don’t remember seeing an Interdictor in the films, so that might be an invention of the EU authors). As far as I know, nobody could ever be assed to even try to define what was happening in hyperspace, which is a good thing, because even in the seventies, physics was advanced to the point where we knew that this was not a particularly plausible proposition.
It’s this kind of complication that leads people to want to draw the genre distinction more on the basis of subject matter than plausibility, because an awful lot of what we would think of as science fiction involves traveling between stars, which most physics will tell you is right out. I would note, however, that Star Trek, The Gap Cycle, and Mass Effect were all at least plausible on the surface at the time they were written. Star Wars was not and wasn’t trying to be, which is where I put the line.
