There is an explicit and an implied conflict in the story "Once Upon a Time." In the story, the family is extremely wary of outsiders, particularly those of a lower class, so they build up a wall around their house. This conflict between the family and the outsiders who move into their neighborhood is the explicit conflict—they try to prevent this perceived threat from endangering their family.
However, the implied conflict is the conflict between perception and reality. Often times, our perception of a threat is more dangerous than a threat itself, which is clearly outlined in the story. The family builds up a wall with razor wire lining the top of it. Their son wants to go outside of the fence, but he gets tangled up in the razor wire and killed—not by the actions of the supposedly dangerous outsiders, but by the machinations of the family. In trying to protect themselves, they became more dangerous, because they interpreted a threat where none existed.