Terminology for Windows domain
Solution 1:
Yes, the WORKPAC is the domain name. The workpac.local is the fully qualified domain name of the windows domain.
In that domain the PCs would be named something like: PC1.workpac.local
As JoeQwerty pointed out the NETBIOS name does not have to match. The NETBIOS name being the "WORKPAC" part of "WORKPAC\user".
As an example you could have a windows forest like this:
/\
/_ \ - WORKPAC.local (forest root/ domain) = Top level
/
/
/
/\
/_ \ - CHILD.WORKPAC.local (child domain)
These would be two separate windows domains within the same logical forest. The NETBIOS name for the child domain would be CHILD whereas the FQDN would be CHILD.WORKPAC.local.
For more information on domain structures check out: Active Directory Domain Hierarchy. The article is in reference to Windows 2000 but the same design concepts apply to newer versions. Also check out Active Directory Domain Names. These should get you in the right direction.
Solution 2:
WORKPAC and workpac.local are both names for the domain. The first one is the pre-Windows 2000 (or NetBIOS) domain name and the other is the DNS (or FQDN) domain name.
http://technet.microsoft.com/en-us/library/cc739093(WS.10).aspx