Let's say we compare two objects and we've already mentioned a particular quality of one of them. Then we want to emphasize that the other object doesn't have that quality. Moreover, let's suppose we are not allowed to mention both objects in our sentence. I would always say "that's the difference from object #1". However, I recently heard in one of the Game of Thrones episodes "that's the difference between X" construction. In that context, X was a person but I doubt this fact changes anything. Frankly speaking, it sounds very weird to me, as my native language is Russian, and whenever we use russian version of between, we always have to mention both objects.
What's the difference between these two constructions? Are they interchangeable? Is the second one even formal or it can only be used when talking to a friend etc?