When working with a workgroup rather than a domain setup, you will have to make sure that each user is added on each machine in the workgroup, or alternatively create one general user, add it to each computer and use it, otherwise a user on a certain machine will not be recognized by another machine unless the user is also added there.
I believe you are able to login using the domain\user method because in the past the computer has been joined to a domain which may no longer exist.
While the computer was a member of that domain, an account has been created using the logon name of the domain and that is why you can keep loggin into the computer using the "domain" account locally.
In order to create new users:
Start -> run -> compmgmt.msc , browse to Local users and groups and add the user there.
By the way, if you have the relevant license for domain services, it's a relatively easy procedure... check this guide to learn how to promote your windows server to a domain controller.