I'll take a stab at it.
A theme is a loose guiding principle. Things are selected that blend together and fit appropriately, but there's not necessarily a concern that the details inform one another or are of any specific importance other than to set a mood, establish an ambiance, or be consistent with the parameters of the area or scene.
A backstory, by contrast, attempts to specifically tie together and quantify each of these items and give them individual importance and a history. It tries to answer why, specifically, each prop is chosen, where it came from, what greater signficance it has, what the history of the building the prop is in has been up to this point, how that building fits in with what's around it and why, etc.
You might consider two Frontierlands as a contrast of these two approaches.
Frontierland, Disneyland, themed: It's the wild west! Therefore, anything that might fit your idea of the wild west is appropriate.
Frontierland, Disneyland Paris, backstoried: It's an old western town called Thunder Mesa, established in year _____ by the Ravenswoods, who set up a gold mine in Big Thunder Mountain, and it's now year ____. Oh, by the way, their house is over there on the hill, but you'll want to stay away as strange things have happened there, and...
When done well, a theme is freeing because you have more options available to you, and many visitors don't care about the backstories anyway. But it may not necessarily be as focused. Undoubtedly there are people at WDI now who seem to feel they NEED that focus to go forward.
Backstories CAN be done well-pretty much all of Disneyland Paris is a shining example of that-but can become convoluted and samey very easily or become fanservice-y in a detrimental way; see, IMO, the continued expansion of SEAS. After a certain point it often becomes more information than the average person needs to appreciate the thing, and then it might seem like too much exposition. It might also put unnecessary or arbitrary limitations on something in a way that a theme would not-the 1930's setting of Jungle Cruise, as an example, or become more important than the actual guest experience. It's my view that modern Imagineers too often forget the power of simplicity with their focus on backstories, and part of the reason the old classics work is that they are presented in a way that is straightforward.
Hopefully that makes sense.