The main difference between the two boys in this passage is the fact that they live in different time periods.
In the first passage, we can identify the setting as the 19th century, and we can also observe that the boy and his family are in the Prairies, traveling to Oregon. The location appears to be the same in the second passage (Chicago). However, the child is not travelling. Moreover, the time period is the 21st century. This means that Chicago is now a developed place, and that the child and his family are able to enjoy modern technology such as a furnace or the telephone.
Nevertheless, we also see that both children face a similar problem. In both examples, the mother of each child is sick and cold, and the children have to find a way to warm her up.