your user (credentials) IS stored on Domain controller. That structure that you can see (documents and settings) is the representation of you user on "local context", since each workstation needs to do that. you stated right, it is NOT your account, its your PROFILE on the local context. Even if you have roaming profiles, when you log on on a station, an "instance" of your roaming profile is created on that station.
BTW, your credential can still be cached by local workstation - that means even you if cant reach the server you can log on on a domain if your credential is cached on that workstation...