Two domains, One DNS, How?

I own two domains. Currently my DNS is serving one of them. I have setup a second set of zones for the second domain... I don't think the second set of zones is working.
Specificily, I made copies the first zone and replaced "every" instance of the first domain with the second. Is that proper? Should a DNS server have have reference to the first and working domain in every zone, even if it is serving two domains? or should every zone state a new domain name for the server regardless of the first?

Note: It is possible that the problem is Network Solutions, I just don't have the knowledge to tell. I have had many problems with them over the years. Network Solutions just will not recognize the DNS name in the second zone. Thus, the domain name is not resolving. The working domain name's registar is dotregister.com.
I am running BIND 8.3.1 on Solaris 9.

If nothing else, If anyone has links to some zone templetes of two domains on one DNS. I can figure it out from there.

Thank you for your help,
Fritz

First to make sure your terminology is straight... A "zone" may contain many "domain's" or more properly termed "hosts".

The "yahoo.com" zone (master) file contains many hosts such as:
www.yahoo.com
ns1.yahoo.com
mail.yahoo.com
etc...

You can also think of a "zone" as a root domain. However, not all zones are the root. But anyway... I'm assuming you own 2 "zones" such as:

zone1.com
zone2.com

Each zone is contained in its own seperate file. They must be named in named.conf with a reference to those master formatted files. Once they are named, it is the master files themselves that determine what and how many domains or hosts you assign to each zone.

Example files which are older versions of my current setup:
http://serialcoders.sytes.net/BIND/