The term "domain name" is used here to mean an arbitrary name in the DNS, and "zone" where there is a distinct separation of authority in the DNS (i.e. there is an SOA record at that particular domain name).
The commerical product called a "domain name" is actually a zone.
For example, www.squish.net and squish.net are domain names, but only squish.net is a zone, and only squish.net has been purchased.
Sorry if that's confusing, but that's life.