In my opinion, the "Major Theme" of a story and the "Moral" of a story are generally, two different things---although, not always. Confused? It depends on the complexity of the story. Take "The Tortoise and the Hare" as one example. A fairly simple, straight forward tale/fable where the "MT" and the "M" are virtually synonymous---ie, slow and steady wins the race, haste makes waste, however you want to put it.
On the other hand, just to use an example you may or may not know, the "MT" of "Ethan Frome", by Elizabeth Wharton, is passion---maybe even understandable passion--- (an older man married to a feeble and demanding wretch, for a young perky woman), but the "M" is basically, bad things happen to people who do bad things (the perky young woman becomes feeble and disabled, just like Ethan's wife, and he ends up having to take care of both of them). The story is arguably viewed as an example of literary "black humor". Other readers think it's just very sad.
So, as a general rule, the more complex the tale, the less likely the "MT" and "M" are the same. In the case of complex works, the "M" is usually an ironic or cynical twist on the "MT".
That help?