Identity can be self-identity or verbal conceptions of ourselves. It is a way of conceptualizing ourselves through the verbal medium, that is through words. Our self-identity is how we articulate ourselves using words and a certain discourse. But we are socialized largely through the medium of language and hence even self-identity is paradoxically external and social:
Social-identity is what we call others' opinions or views of us. It is important to note how the social and the personal / individual interrelate. Our understanding of ourselves (self-identity) depends on language and on words, therefore on a discourse and that discourse is given to us by society. It means that we cannot have a conception of our own identity in isolation. Our understanding is deeply informed by the understanding or by the gaze / look that is given to us by our social identities.
Moreover, identity is not once and for all given to us. Stuart Hall rightly describes identity as “a temporary and arbitrary closure of meanings” (in Barker). So every time society attributes to us our identity, it is not absolute but only a temporary one. Here Hall is suggesting that identity is negotiable . There is mobility to move within a certain framework since our description in language is plastic, that is flexible and anti-essentialist.