You are right that there is something more! One of the commonest mistakes on italki is the question 'What is the difference among these three sentences?' rather than the correct form 'What is the difference between these three sentences?'. Even very advanced learners seem to think that 'among' is the correct word here. I think that there must be some grammar books somewhere in the world perpetuating the myth that 'between' is for two objects and 'among' is for three or more. This is totally untrue.
In fact, the difference is this: If you are considering the different elements separately ( sentences, houses, people, trees) you use 'between'. But if the elements are an undifferentiated mass - like a crowd or a disorderly jumble of papers -you use 'among'.