How do children learn about the differences between what they see and what other people see?

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.