Generally, book publication presents a single version of a character whereas periodical publication and screen adaptations present multiple versions. However, there is a long history of different versions of a story. Hesiod and Homer present alternative birth stories of Aphrodite; Plato rationalizes them.
The Smallville and Arrow TV series present different versions of Oliver Queen played by different actors. Smallville is a prequel to a version of Superman but not a version that we have ever seen before. Everything important is happening before Clark dons the costume or flies, even Lois Lane knowing of his powers and agreeing to marry him.
There are two versions of Poul Anderson's Kith History (see here) and a few stories in his Technic History exist both in an original version and in a version that has been revised to make it consistent with the History, e.g., "Margin of Profit" (see here) and "The White King's War" (see here).