What mostly causes Bruno to recognize that he and Shmuel are dissimilar?

In The Boy in the Striped Pajamas, Bruno finally recognizes that he and Shmuel are dissimilar when Gretel corrects him on his pronunciation of "Out-With" to Auschwitz and explains that the Jews live on the other side of the fence to stop them from mixing with other people. When Bruno further questions Gretel concerning what his family is, she responds by saying they are the "opposite" (183). Before this episode, Bruno thought the children chose to remain on opposite side of the fence.
However, ironically, it is shortly after this discussion between Bruno and Gretel that the children discover they have lice. When father shaves off Bruno's hair, he realizes that he looks more like Shmuel than he thought before. Therefore, even though Bruno finally begins to realize the differences between himself and the children on the other side of the fence, he also begins the self-realization that he and Shmuel are alike in many ways on a deeper level, which foreshadows the end of the novel.