Science Fiction: "Fiction that imaginatively uses scientific fact and speculation to create a fantastic situation." That's what Webster says, anyway.
Sci-Fi: the term often used by the commonfolk to refer to those silly stories about spaceships and monsters, even if most such stories are really about something entirely different and probably not very silly at all. Usually.
While writers of science fiction have recently (by which I mean the past thirty years or so) moved away from what is perceived by the public to be "sci-fi", writing much more about people than monsters, movies and television still dwell on themes exhausted by hacks in the fifties. Consequently, those ignorant of the genre still dismiss most works of sf as "that silly sci-fi stuff," while those of us more informed cringe at that hideous neoligism.
So what good old Hollywood gives us is Star Wars, which isn't much more than swords and sorcerers at FTL speeds, with X-wing fighters making U turns in vacuum. It gives us Back to the Future, in which a time travelling DeLorean saves the day for a bunch of cardboard cutouts. Television gives us a new Star Trek clone every year, none of which offer us anything as far as originality or interesting variations from the original. Film gives us The Ice Pirates, Wierd Science, and Godzilla vs. Mothra. It gives us sci-fi in all its silliness. Hugo Gernsback would be proud! Harlan Ellison pretty much summed it up when he said "As fit subject matter for motion pictures, science fiction and fantasy are a pair of dead ducks." (He of course retracted this statement after seeing Brazil, which he promptly claimed was one of the ten greatest motion pictures of all time, along with about two-dozen others.)
While Hollywood garners all the big bucks for its sci-fi, it ignores whats happening with written sf. Recent sf writers are taking the best elements of the Golden Age and the New Wave and creating something totally new and original, and doing it with real skill, but movies are still doing sci-fi. Movies have ignored Gene Wolfe, Ursula LeGuin, William Gibson, Dan Simmons, and hoards of others in favor of remakes of schlock. Gems like Bladerunner come along far too rarely. We can only hope sci-fi will eventually mature into science fiction.