Both Bruno and Shmuel lived during WW2. They were exactly the same day, April 15, 1935. They were both forced to live in Auschwitz.
I think the biggest difference is why they moved to Auschwitz. The reason why Bruno had to move to Auschwitz was because his father's work. He was an important Nazi officer. But Shmuel was a Jew who had to live in the concentration camp.
Bruno was a rich and spoiled kid, but Shmuel was a poor little boy. We can for example see that on their clothes.
In the beginning Bruno and his family moved to Auschwitz because of father's work. Bruno did not want to move, but they had to.
When Bruno arrived the new house he went outside exploring. He found a farm with people who wore striped pajamases. One of the people behind the fence was a little boy named Shmuel. Bruno and Shmuel became best friends.
In the end of the book Bruno promised to help Shmuel find his papa. Shmuel found some clothes for Bruno, so it looked like he also was a Jew. While they were searcing for papa there came some soldiers and brought them to a small room with lots of other people. Everyone were screaming and screaming, but no one outside could hear them. There came some gas, and everyone in the room died, included Bruno and Shmuel.