The Primary server is the server that was configured by a human being, and contains a complete record of the data for a particular zone. A full copy of the zone file. Any nameserver which does not contain a full copy of the zone file for a domain is not authoritative for that zone. It is usually not possible for a server which is primary or secondary for a domain to NOT be authoritative for a zone. The most common errors are forgetting to properly format the SOA record at the beginning of the zone file.
Recursive servers continue to ask additional servers for an answer.
Non-recursive nameservers check their own database and then stop. A recursive server is a good server to point desktop clients to for Internet resolution. A non-recursive server is ideal for placing outside on the Internet for resolution of your own domain and nothing else. Your domain's information is stored in one or more zone files on your authoritative server. This zone file defines all the public names and IP addresses you wish to be resolved.