Which Is the Real Story?

Recently, my wife and I watched again Peter Jackson‘s films of The Lord of the Rings, J. R. R. Tolkien‘s masterwork. Now, we are watching the films with the director’s, producers’, and writers’ commentaries. The question that immediately arises when one watches a movie based on a book that one loves is whether the movie does the novel justice. Does the movie tell the same story as the novel?
We have enjoyed the story of The Lord of the Rings in three media: Tolkien’s novel, Jackson’s film, and the BBC’s radio production. I have read, viewed, and listened to each of these many times. Is the story the same in each medium?
The answer is "No," if by "the same," one means that the movie and the novel are identical in each detail. Given the differences between a film and a book, it is impossible that the two be identical.
The answer is "Yes," if by the "the same," one means that the movie and the novel tell the "same story," however different the two may be in detail. For The Lord of the Rings, my judgment is that Peter Jackson does tell the same story as does Tolkien. For that matter, the BBC’s radio production also tells the same story.
Consider this possibility: the "real" Story lies behind any particular telling of the story in any medium. While we can consider Tolkien’s novel to be the canonical (authoritative) version of the Story of the destruction of the One Ring, the other versions can still tell the Story, although different in detail from the canonical version.
The BBC radio production is very close textually to the novel. (Ian Holm plays Frodo in this version, and, of course, he plays Bilbo in Jackson’s films.) But the radio version omits the Old Forest, Bombadil, and the Barrow Downs just as does Jackson’s film. Like most readers of the novel, my wife and I both delight in Tom Bombadil and Goldberry; yet I understand why someone telling the Story in a different medium would omit them.)
An analogy for the relationship of Jackson’s films to the novel: we can see the films (and the radio production) as remixes of the novel, just as musicians remix songs and albums. Actually, musicians may release a song in versions of different lengths; in such a case, do we ask which version is the "real" song? Really, we decide which version we prefer. Realistically, isn’t that what people do with novels and movies based on them?
Here’s a last question, which I only mention: how much can a version (or remix) of a story change it without making it a different story? It’s a question that I and the students of a course in the fantastic in literature and film discussed without arriving at any kind of definite answer. The answer is surely up to the individual.