No, there is a separate field for each on the User form, though we hide the Domain field in the default implementation, and the two fields are kept in synch. Associating a Company record to a User will associate the User with the Domain that is associated to the Company automatically. This allows you to declare overrides by declaring a Managed Domain if needed, but otherwise ensures that the User has the same domain as their Company.
For example, there is a Domain field on the Company table. If the Domain for "Company A" is set to "Domain A", then all users associated with "Company A" will be in "Domain A". The Company and Domain usually will have the same name as well, at least in our default implementation, though they can be different.
We do have an older tool called Company Separation that just handled domains through the company record, but this is legacy and no longer supported. You would be better off going with Domain Separation.
