Some writers try to make their own versions of classic legends like Atlantis. Others are unique to one author, such as J. K. Rowling's world of the Harry Potter series; they remain unique partly because of copyright.
It can be argued that every work of fiction generates a world of its own (Robert A. Heinlein coined the neologism Ficton to refer to such a world) but to qualify as a fictional, alternative reality the setting should be distinct and germane to the stories told there.
By their very nature, fantasy and science fiction tend to generate fictional realms, but they may also apply to other types of stories where the time and place in which stories are set invokes a sense of a world apart and unique to the purpose of casting the tales told in it.
See these types:
Other fictional universes:
See also: Virtual reality