To me, the difference that matters between sci-fi and fantasy is that, even when sci-fi uses science or technology that we currently believe to be impossible, there is always the underlying assumption that, in the story's world, it is real science and the technology is based on real science. That is, the studies have been done, the theories have been developed, and the technologies have been derived, in complete accordance with the underlying laws of the physical universe. At no point in a real sci-fi story - no matter how far-fetched the technology - is the reader asked to believe there are supernatural phenomena at work.
Of course, as far as I'm concerned, the closer to real physics it is, the better, but the main point is the assumption that real physics and nothing else, is what makes the universe work. Once you introduce anything supernatural, it stops being sci-fi and becomes fantasy - and it doesn't matter if it's in the far future, on spaceships, or distant planets, supernatural forces are by definition outside of physics and therefore have no place in science fiction.
In fact, I'd go farther still and say that if something we once believed to be a real physical phenomenon, or believed might be real, has been conclusively shown by science to be a false belief, that should not be included in sci-fi either. The best example of this I know is "psi" phenomena (telepathy, telekinesis, clairvoyancy, etc.) which have been well and truly debunked over and over again. Their inclusion in modern sci-fi must therefore count as introducing the supernatural. (However, sci-fi of the fifties, sixties, and even the early seventies, still counts as sci-fi because the question of the reality of these phenomena was still an open scientific question at the time it was written.)