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My djinn world uses the same physical world we live in, on a different plane. Maybe I can explain it better with this example: The djinn world shadows ours, and in someplaces it overlaps. They don't see us and we don't see them, except in the overlap.
Isn't a parallel world something separate entirely? With a copy of everything, including the people?
The other day I was editing and I hit a roadblock. (Sci-fi and Fantasy writers: Help me out here!) I keep writing about a parallel world, but do I really mean dimension?