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'.

Here is a good explanation of the difference http://www.quickanddirtytips.com/education/grammar/between-versus-among

This is a good explanation, which comes with a quiz: "We say that somebody or something is between two or more clearly separate people or things. We use among when somebody or something is in a group of people or objects which we do not see separately. Read more at http://www.englishpractice.com/quiz/exercise-11/#q326oC8Vcc5wRO2Q.99" Often when there is a group of more than 2 things, the group is not seen as individuals but as an unindividuated mass. But not always. I hope this example demonstrates the point: He divided the sweets equally between all 20 children. He went among the children, giving each one an equal share of the sweets.