Well, generally the difference between fantasy and Sci-fi is believability: Sci-fi can technically take place in our universe and should conform (however loosely) to our laws of physics, so Sci-fi always generally explains or handwaves the more exceptional constructs in their universe in a way that, loosely speaking, would be possible for us to do in our universe.
An example would be element zero of Mass Effect, which is used in a pseudo-scientific way to explain why the ships travel so fast, and how everything is powered, why the guns shoot so hard etc. Techinically, if that element was found by us, we could achieve those things as well.
Fantasy does not bother to justify itself in our universe, so you get magic and situations that are never explained or justified, they just are the way they are.
Skyrim is chock-full of unscientific stuff that is never reasoned or justified. It's just possible because 'magic'. This is pure fantasy.
Oddly enough, the most interesting case when you consider these definitions is Star Wars, which has the Sci-fi elements as regards the hyperdrive engines, all the guns, armour, alien races etc: It's justified by pure pseudo-science, but the Force and the origin of the Jedi's powers is pure fantasy; a mystical energy that has no scientific basis, and allows basically anything to happen no matter if it's scientifically possible or not. And even more interesting is when you consider Lucas' abysmal explanation of the Force as the midichlorian bacteria that lives in all things and gives a Jedi power, that was essentially an attempt to remove the fantasy side of Star Wars and make it a 100% rational Sci-fi, but it didn't work because the explanation wasn't plausible enough, and it came too late in the game, so the inexplicable fantasy nature of the Force was already accepted as what it was.