You can log on to a window 2003 server easily, and each time it will give you same session, called console session. If you log on to the same server remotely, it will start new session, it will not give you the same console session.
If you want to access same Console session remotely, same as original server session just use /console switch in mstsc command. For example if your server name is, myServer type the following command:
mstsc -v myServer /console