Domain Name Servers on the internet use various software to function, the most popular DNS server type on the internet is BIND, which stands for Berkeley Internet Name Domain. BIND is the predominant system on UNIX based systems.
BIND was originally created at the University of California, Berkeley and is maintained today by the Internet Systems Consortium. It was rewritten to address architectural difficulties and also to support DNSSEC (DNS Security Extensions).
BIND initially supported only flat text files to store and retrieve data. However, recent versions of BIND have allowed zone data storage and retrieval in a variety of database formats including LDAP, PostgreSQL, MySQL, and ODBC.
Since BIND was written a long time back, there were many security vulnerabilities that have been exploited by earlier versions of BIND and hence their use is strongly discouraged. The latest version of BIND should be deployed, although they have also experienced numerous vulnerabilities which can be managed to some extent by using DNSSEC and other technologies
More information about BIND at the ISC website can be obtained from https://www.isc.org/software/bind
Google Public DNS is a proprietary implementation of the DNS standards and is not based on open source software such as BIND.
I can foresee Google public DNS becoming an open source product