How do children learn about the differences between what they see and what other people see?
I am going to go psychological with this one because I think it's fascinating. The idea of children gaining self consciousness is a powerful reality. For many, it marks the moment when a child's innocence disappears and the narrative of experience takes over. It is this gap in perception that helps to bring the onset of adolescence and perception. I think that children are gaining this insight sooner than in the past. Part of this is because they are exposed to much more information and a proliferation of different perceptions at a younger age due to the onslaught of technology and the access to it. There is no exact time as to when this happens, but rather is a process that happens in the psyche of the specific children. Sometimes, this is brought on by their own social interactions with other children. It could be something small. Perhaps, a child brings a treasured item to school and others make fun of it, causing the child to see the item in a different light than before. It might be something significant, such as a family trial or challenge that permanently alters how the child sees themselves and how they see the world. It might come with sheer understanding or knowledge, something a child learns in school sticks with them and causes them to see themselves and their world differently. When it happens and even how it happens might pale in comparison to this instant, itself. The moment of self awareness and self consciousness, when it happens, permanently alters a child's perception of themselves, others, and the world.
It's difficult to tell from your question if you mean what they physically are able to see, their perceptions of reality vs. those of adults or how the role of imagination and mental immaturity affect their perceptions.
I can modify this answer if you specify more directly what you are looking for.
My sense of the psychology and physiology of this comparison is that children lack the ability to reason at an adult level, the ability to completely care for themselves, a lack of vocabulary to attach to their senses, and are in the beginning and middle of the socialization process.
So I would think children learn how to interpret what they see over time as society, their parents and family teach them how to perceive what they are seeing. A child who sees another child hitting someone might think it's funny at first, until they are taught that violence is wrong. This takes time and repeated conditioning, and as a child's brain and education begin to mature, the socialization accelerates.