In the story, “The Red Convertible,” by Louise Erdrich, what contrasts does the story draw between the world of the reservation and the white American society beyond?

There isn't very much description of the reservation in this story, and most of what we can say about the reservation is implied rather than explicitly stated. For example, when Lyman and Henry take off in their convertible and drive off to "see . . . the sights", the implication is that the society beyond their reservation is full of curiosity. Indeed, they drive for "one whole summer." This implies that there isn't, by contrast, very much to see and do on their reservation. Later in the story, Lyman describes the roads on the reservations as "like government promises—full of holes." The implication here is that the reservation is very rustic and not as developed or advanced as much of the society beyond the reservation.
Another indication we get as to the differences between the reservation and the world beyond it is when Lyman's mother says of the hospitals beyond the reservation, "They don't fix them in those places . . . they just give them drugs." The implication here is that the people on the reservation have a different, perhaps more traditional attitude toward medicine and healing, and that hospitals beyond the reservation simply prescribe drugs to treat symptoms, without trying to heal their patients in any meaningful sense.