Another way science fiction compares to fantasy is that fantasy uses nonhuman characters and fantastic creatures, like talking wolves, griffins, dragons, elves, dwarves, fairies, etc. Science fiction also has its share of nonhuman characters: the mutants in X-Men, the T-800 in The Terminator, Robby the Robot in Forbidden Planet, the apes in The Planet of the Apes, the wives in The Stepford Wives, and every kind of alien. In both science fiction and fantasy, these creatures are anthropomorphized--i.e., they have many human characteristics and sometimes even act exactly like humans. Even if they don't outright talk and walk on two legs, these creatures are typically more intelligent and in tune with humans than those of our own world.
So what's the difference? Fantasy creatures are all "what if?": what if people were half fish (mermaids), what if there were giant fire breathing lizards (dragons), what if the fields are full of tiny magic people with wings (fairies), etc. These creatures are not possible. Science fiction creatures, on the other hand, are not only possible but many are probable in the near future: if we keep making robots (T-800), if we keep searching for extraterrestrial life (aliens), if we keep experimenting with animals (race of apes), etc. Most of these creatures are a result of mankind looking to move beyond their own human limitations. Peter Weyland was looking for immortality and instead found Xenomorphs. Cyberdyne Systems wanted a better soldier, so the Terminators were created. Seth Brundle wanted to create instant matter transport and tragically devolved into the Brundlefly.
Perhaps nothing illustrates this difference more than the difference between Dracula and Adam, Frankenstein's monster. Dracula is a fantasy character: as part of an ancient race of vampires, he can magically transform and bend the laws of physics (no reflection in mirrors, can move shadow independently of self, etc). Adam is a science fiction character: he was brought to life through an experiment with chemicals and electricity restoring him to life. Though both are really horror characters based on their story plots, it's clear by a nonhuman character's origin if they are fantastic or scientific.
A related point while we're at it: sometimes the people in your story are the extraordinary creatures themselves. In Lord of the Rings, some people are human just like us, dear reader, while others are dwarves, hobbits, and elves. These types of characters are not really human but not creatures either--at least not in the sense of orcs, dragons, and the walking trees of Middle Earth. That's another good point: plants can be extraordinary creatures in fantasy, even if they don't walk or talk. A plant that provides a miracle cure not found in real life or that can attach to a person and make them act out their deepest desire are just as fantastic as seals that turn into women or wolves that can huff and puff and blow a house down.