So, now that various terms of identity have been identified, how are they to be used? One use is in the critical analysis of speculative fiction. A number of examples exist of what may be termed identity crises - situations where manipulation of various forms of identity ensure that specific identities don't match in a traditional human way. Spoilers follow.
1) William Gibson's Mona Lisa Overdrive. One primary character is Angela Mitchell. She is a simstim (simulated stimuli) star and a noted celebrity. She enjoys a consistent identity structure throughout most of the book. The central plot involves a conspiracy to abduct her.
Another primary character is that of Mona Lisa. She is SINless - lacking a government issued Single Identification Number. She lacks a document identity. This is a latent identity crisis in itself. Lacking such a SIN, Mona is unable to assert her identity before any government agencies; she is effectively a non person to such agencies, and her disappearance will not be noted or followed up on.
Mona also superficially resembles Angie, a resemblance that is compounded when a cosmetic surgeon specifically reshapes Mona's appearance to Angie's. This is a crisis of bio-metric identity: two persons who share one bio-metric identity although the sharing is not perfect; Mona's fingerprints are not Angie's, and in fact Mona takes comfort from the fact that upon close inspection and familiarity, Mona's hands do not resemble Angie's.
At the conclusion of the book, Angie has been abducted, brought to the same location as Mona, and has died. The corporation that Angie had worked for succeeds in rescuing Mona and recovering Angie. A representative of that organization chooses to accept Mona as a stand in for the deceased Angie. As the book ends, Mona has replaced Angie in the role of Angela Mitchell's identity.
Mona thus retains psychological identity: she identifies herself as a unique ego, with continuity of memory as Mona. Bio-physical and genetic identity are maintained for Mona - she still exists in the physical body she has always inhabited, with its own unique genetic code. Bio-metric identity is split - superficially Mona now owns Angie's face and other biometric recognition cues, and presumably SenseNet the corporation has erased all of Angie's other bio-metric files and replaced them with Mona's.
Mona has assumed Angie's social identity traits. Mona now owns all of Angie's possessions, and has document (and presumably code-string) identifies as Angela Mitchell. However, one character indicates that Mona differs in stylistic identity from Angie, such that an aware or critically trained observer can detect a difference.
2) William Gibson's Idoru. The idoru, Rei-Tomei is a Nipponese pop starlet, without physical form. Using the terms of identity, she lacks a bio-physical and genetic identity, not owning a consistent physical form. She does enjoy geographic identity, given that there exist any number of holographic projection devices with which she can appear to manifest a physical existence. She does, however, have a unique bio-metric identity. Through doctored photographs and video media, she possesses a unique appearance.
As she has a name, Rei Tomei owns a very weak form of social identity. Presumably, she also maintains a consistent stylistic identity, as all of her musical endeavors are constructed by other people with the intent of maintaining a consistent style. As a corporate person, I presume she owns various codestring identities that the corporation uses to establish her bank records and so on.
Left ambiguous in the book is if she enjoys a single ego-identification. Written and electronic records might be used to maintain a continuity of memory, as well as the individual memories of the persons who create and operate her corporate identity.
3) Steve Jackson's Games GURPS and Transhuman Space. In the universe of both these works, it is heavily implied that personality, sapience, and intelligence (both 'natural' and artificial) are connected to software, rather than hardware. In that universe, it is technologically and metaphysically possible for a personality to change physical bodies through the appropriate techniques.
Such a transference allows a change of bio-physical (and presumably genetic) identity. Depending on how the physical form is constructed, bio-metric identity may or may not change - a personality moving from one artificially constructed body into another with the same bio-metric features will enjoy a consistent bio-metric identity.
Social identity in such a context becomes very ambiguous. Various forms of social identity that are tied to biological identity become fairly meaningless. The only strong consistent measures of social and informational identity become data-point and codestring identifies. Presumably, a single ego-identification would wish to keep these forms of identity unique onto itself, and these forms of identity would have to form the basis of other forms of social identity.