I think that the similarities might be a form of the Texas Sharpshooter fallacy. That is, there are many millions of creative works in existence throughout all time. With that many, you are bound to find multiple examples of pairs of works that have similarities, even if the creators were unaware of each others' works.

Non-creative works of the same fallacy include the Lincoln/Kennedy comparison, the one book (can't remember the name) that seemed to predict the sinking of the Titanic decades earlier, and the various Nostradamus "predictions". Also see the Birthday Paradox.