when logging on to a computer that is part of a domain you need to specify if the user-id is a domain or local user id. You do this by either specifying the domain name or not specifying the domain.
When you are at work, you are most likely logged on using a domain ID, which will automatically get passed to the server you are attempting to connect to.
When you are at home, it would automatically pass the user-id and password that you are logged on to your computer with, which I would assume is not your work domain user-id and password.
When you just put in "user" it is assuming a local user-id on the computer you are attempting to connect to, which may not be a valid user-id on that server. If you put in user@domain then it will validate against the domain security store.