It's the same for the dreamer. Every visual element in the dream may be a representation of some aspect of the dreamer's identity. Each character and object in the dream is a split off or dissociated component of the self - but the dreamer is not fully aware of this. Dissociation is a common phenomena in cyberspace at large. It is a well-known fact that people use the internet to express and experiment with various aspects of their identity.
Some people deliberately create a specific online personality for themselves.
They have some conscious control over the same kind of wish fulfillment that fuels dreams. For most people, it's definitely NOT schizophrenia, but it IS a splitting of identity between what one usually presents to others in the physical world and what one likes to create in the cyberworld. All are aspects of one's identity, although some may be hidden or unconscious aspects. Both were equally real to her. For example, online gender-switching is a fairly common practice.