How is the term identity distinguished from ideas like personality, character, psychology, self, soul and individuality?
In the analysis of culture or literature, when we use the word identity we mean something very specific:
Location, Location, Location
When you need to "identify" yourself, you would do so in ways that map your location in the scheme of society and history: your name (mapped by family, in public records), your address (mapped geographically), your occupation (mapped in the economy), your relationships (mapped in society).
Style is Substance
In addition to the above, we culturally identify ourselves when we choose what to wear each day, how to comb our hair, the ways we talk (or ways we don't talk), who we spend time with, the music we listen to, the types and brands of food we eat and beverages we drink. Rather than suggesting the expression of an inner self, the term identity, therefore, denotes the ways we adopt and use external facts and "signs" to ally ourselves with socially recognized groups, styles, classes, regions, nationalities, subcultures, and so on.
"Identity" is Not Coherent or Permanent
Since any one person is a member (would-be, current, former, vicarious) of many groups and social categories, identity is never coherent, unified and permanent. It is necessarily pieced together, negotiated, ad-hoc, provisional. Everyday we identify and re-identify ourselves--often unconsciously. Not only do we re-evaluate and shift our location on the map of society and history, the map itself is constantly changing.