Maybe this can clear things up for you. In windows DOMAIN refers to three things:
1.) The Domain naming context in the Active Directory ldap store. (DC=child,DC=root,DC=top.com)
--- This follows RFC rfc2247
2.) The kerberos realm that uses the the ldap store.
-- realm name is something like @domain.com...user principal name is firstname.lastname@example.org
3.) The DNS domain domain.com
-- DNS resords for domain.com in the typical fashion.
It's best practice (and the default with the GUI based tools) for all of these to match. They don't actually have to. You could add any number of different UPN/SPN suffixes for user/service accounts. The DNS needs to work, meaning that it could be different from all three as long as the SRV records actually resolve correctly.
Anyway, I have found that breaking it down this way usually helps when discussing AD with my UNIX'y brethren.