Mind if I chime in?
griffinp, I totally understand how you could understand "parts" as being an aspect of DID. Honestly, I felt the same way in the beginning and told my T - I have a lot of issues, but I don't think I've got DID. (At that point I think she probably realized there was a miscommunication

)
I'm just beginning this "parts" stuff in therapy. Started two sessions ago actually... basically it's like emotional states. For me, I've got a child (about 7ish) and a teenager (about 13ish) and then just me. I always say that the child cries too much and is far too sad and lonely, the teenager is really hurt, abused and mad and then me... well I'm the "adult" so I try to be rational (which fails, more often than not).
I can't really distinguish them. Only after a visualization exercise and my T asking me how old I *felt* did I begin to distinguish between these different aspects of myself. And actually, it makes a lot of sense to me now, considering what I've been through and the events that are tied to those ages.
All I know is that when I feel like a kid, I can't look at T, I feel scared and really small. Then when I feel like a teenager, I feel hostile and agitated and just way too emotionally volatile. Then me, I try to be unemotional and rational (which fails, since I'm realizing I stuffed the emotional stuff down inside which is why I'm having difficulty with this "parts" stuff now)
The child is stuck wanting love and to feel safe and now alone or abandoned, the teenager wants to be left alone but wants people to know she's suffering and angry and sad, and once again me -- well, I admit I ignore the two of them more often than not. Or at least I realize that now
I really like the "Wounded Self" article below actually.