A shadow, as seen in Persona 4, often calls itself the “True Self”. Many things the shadow says reflect or are based upon the character’s true feelings, but can also be exaggerations or metaphors masking the character’s true feelings.
In the end, however, the shadow will eventually show its true colors— and the character’s. The shadow is often a representation of personal facets that a character has rejected, and brings a character further away from their “Persona”, or their “Ideal self”.