In projective identification, you become the aspect (either distortedly elevated, or distortedly sullied) that is the disowned part of another person’s mind. The seemingly paranormal side to this dynamic is that you can start to become, in words or action, just exactly what the other person thinks you are — even though you were never really that in the first place. It seems like a kind of magic (and a way of knowing what is in the other’s mind without him telling you).
In the case of Althusser’s notion of interpellation, the authorities, or an authority within the social system “hail” you. You don’t know that you have a particular role and identity to play until you are thus hailed. Once this happens, you understand that you are exactly that sort of person that the social system thinks you are because of your own reflexive response to being addressed authoritatively. You implicitly accept the right of the authority to give you an identity, and your own reflexes betray you into falling into line with whatever identity is given. In the case of Althusser’s paradigm, you probably didn’t have a sense of self before you were interpellated in this way. In the case of Klein’s theory of projective identification, your actual identity is being distorted by this psychodynamic.