Everybody knows that H. G. Wells is one of the pioneers of science fiction. He wrote The Time Machine, The War of the Worlds, The Invisible Man, The Island of Doctor Moreau, and so on. Here's what he had to say about the distinction between Science Fiction and Fantasy.
“Hitherto, except in exploration fantasies, the fantastic element was brought in by magic… but by the end of the last century it had become difficult to squeeze even a momentary belief out of magic any longer. It occurred to me that instead of the usual interview with the devil or a magician, an ingenious use of scientific patter might with advantage be substituted… I simply brought the fetish up to date, and made it as near actual theory as possible.” 
In other words, he took fantasy tropes, and replaced the magic with science. Otherwise, the stories were the same. So the difference between SF and Fantasy, in its modern incarnation anyway, was that one uses chemistry and the other uses little magic devils to produce a counterfactual scenario that the story can explore.
Fantasy and SF are in essence the same thing, but with different decorations. They share the same bones, but have different skin.
According to the best physics we have, it's not possible to travel faster than the speed of light. Not today, or ever, at least until the laws of physics change. Yet, many SF stories include spaceships with drives that move the ship faster than the speed of light. Star Trek style warp drives, Star Wars style hyperdrives, etc.
There is no practical distinction between doing the impossible by traveling faster than light, and doing the impossible by shooting lightning from your fingertips. It's magic in either case. SF merely couches this magic in pseudo-scientific terms and decorations (see the Wells quote, above) as part of what amounts to a fashion choice.
Personally, I think of fantasy as a broad category that includes any type of story that posits a counterfactual world in order to explore what the world would be like it it were true. Under that broad category are things like medieval fantasy, horror, and science fiction, among many others. These subgenres are mainly distinguished by having their own set of recognizable tropes, styles, themes, and so on, but are not fundamentally distinct from each other.
 (From an interview quoted in Trillion Year Spree by Brian Aldiss)