DID can be misdiagnosed as other psychiatric categorizations, or it can also be what psychology calls "comorbid" with other so-called disorders.
It is common for various individuals in a system to have different eccentricities and behaviors, to experience life differently. Sometimes it goes as far as having a "personality disorder."
Personality disorders are classifications of personality traits that cause a person to behave in a disorderly fashion. Generally they are dysfunctional thought patterns and patterns of behavior than are deeply ingrained in the personality and difficult-to-impossible to change. Usually they are rife with misperceptions of reality that bolster denial or self-delusion, so that the person with the personality disorder may have a very hard time realizing there is a problem or changing their behavior.
That's not to say that they can't be worked on, but that the psychology literature on the subject has been invaded by the fact that if the people with personality disorders don't truly wake up and smell the coffee, there is little anyone can do to change them. Problem is that this is generally true of anyone anyhow -- with the caveat that psychology is lumping these people together because the undesireable behaviors are particularly resistant to treatment and likely to relapse after they are worked upon.
DID used to be Multiple Personality Disorder -- it has been pulled out of the personality disorder category and placed under dissociative disorders as of the DSM-IV.
Individuals within a multiple system may have personality disorders.