Fantasy allows an equal or even broader sweep of imagination than "hard" SF, where anything goes so long as the worldbuilding is done carefully and plausibly. Maybe pigs can fly on Etavin, but the author had better lay a pretty thorough groundwork for it, so that the reader accepts this, rather than rejecting the idea and the book. Fantasy encompasses everything from traditional swords and sorcery to vampire stories. Anything that puts a kink, small or large, in "reality". Whatever that is.

Fantasy is the oldest form of fiction, starting with heroic quests like that of Gilgamesh, and including the tales of the War at Troy, complete with talking horses and ghosts. Most fantasy depends on magic of one type or another, perhaps several types in one book. Some worlds allow their characters endless permutations, like T.H. White's Merlin conjuring all sorts of things for young Arthur in The Once and Future King. Other books take a narrower view, and those are harder to write, because there are so many more strictures on what the hero can use to get himself out of trouble. On the other tentacle, it's easier for the author to keep the protagonist IN trouble, if magic cannot do all.

Soft SF can have elements that seem to be part of the fantastic but are not, in that perhaps, like Anne McCaffrey's world of Pern, the place was founded by spacefaring people from Earth. Science created her creatures called dragons, and there is nothing magical about the dragonriders except her deft storytelling. Pure fantasy runs toward Lord of the Rings by J.R.R. Tolkien, or in the total opposite direction: Metal Angel by Nancy Springer. Both of these depend upon some element of non-science to make the plot work. If you call your magic magic without a qualm, it is fantasy. If you call it psionics, you're probably soft SF or science fantasy.

There are endless permutations on the fantasy genre. There is such tremendous crossover in the elements of fantasy that it is sometimes impossible to stick a book into a single classification. Some may quibble with our categorization, and you may see some of these twice!

Heroic Fantasy, also known as Swords & Sorcery or Epic Fantasy
Gentle Fantasy, also known as Magical Worlds
Gritty Fantasy
Dark Fantasy
Historical Fantasy