Dissociation can be part of PTSD, but sometimes when it's severe or pervasive enough, it can become a separate diagnosis. It's all under the same trauma umbrella, though. Not everyone with PTSD dissociates, but everyone I've ever met who dissociates has PTSD. It develops in response to trauma.

There are more types of dissociative disorders than just DID, so you don't have to have separate parts to have a dissociative disorder. There's a whole range of dissociative experiences, and DID is just on one end of the spectrum. There's a lot in between.