I think the Serling Quote on Wikipedia sums it up pretty well....Rod Serling claimed that the former was "the improbable made possible" (Sci-Fiction) while the latter was "the impossible made probable" (Fantasy)
I usually just use it as a term for how tight the technical aspect of the show/movie is. If the movie is completely disinterested toward the technical side, then it's a fantasy where "Sciency" stuff has replaced magic. While Sci Fi is very into the technical side, and the actual "how things work" can have huge (And almost always does) impacts on the story. It's just another way of saying this is very, very loose Science fiction, where as say, 2001 was very tight.
Science fiction is generally rooted in science; either modern science, near-future science, or plausible future science. The other VERY important part of science fiction is that it's part of speculative fiction, and speculative fiction asks questions.
A good example of "the question" part would be, "What would happen if people became fast healing and virtually immortal?" Now, somewhere in that story, the "HOW?" comes into play, and this is what separates Science Fiction and Space Opera (aka Space Fantasy).
Science Fiction would have no problem doing the research. SCI-FI looks up where we are with medical nanotech and biotech, because that shit is cool and science fiction is the domain of nerds. SCI-FI talks to experts in those fields and ask them to postulate where that technology will be in 10, 20, 50 years. Then they take an interesting nugget of that information and write a story.
Fantasy doesn't do research, it invents stuff. Fantasy doesn't look at modern technology, they use plot devices that usually aren't rooted in any science. They don't talk to experts because
everythingan expert will tell them will ruin the story
that they already came up with.
Star Trek: TOS, TNG, DS9, VOY, ENT = Mostly Science Fiction. Mostly.
Star Trek [2009] = Space Fantasy
Star Trek: Into Darkness = Space Fantasy
And that's perfectly OK for probably 90% of the people who see those movies, and 100% of the studios. I really liked the 2009 flick when I first saw it, but on repeat viewings I found more and more that didn't sit well with me, until I got to the point where I am now. Star Trek and Star Wars are, for all intents and purposes, the same now. And that's perfectly OK for probably 90% of the people who like those movies. But for the 10% that loved Trek because it wasn't Star Wars, these new movies are nerd-rage inducing.
That FAQ that was linked to earlier? Yeah, that guy is a Trekkie. He's part of that 10%. It's fun to mock him, but I didn't notice many of you refuting much of what he wrote! Reason? Because most of what he wrote cannot be refuted. Most of what he wrote was objectively true.
I really liked STID on my first viewing. Next time I see it my subconscious is going to pick that fucker apart and I'm probably going to end up thinking it's just "OK", just like what happened with the last film.