PostgreSQL is a powerful object-relational database system. It is open-source and runs on all major operating systems, including Linux, UNIX (AIX, BSD, HP-UX, SGI IRIX, Mac OS X, Solaris, Tru64), and Windows. It supports text, images, sounds, and video, and includes programming interfaces for C / C++, Java, Perl, Python, Ruby, Tcl and Open Database Connectivity (ODBC). It is developed by a worldwide team of volunteers and is not an entity of any corporation.
MySQL is a relational database management system, whereas PostgreSQL is an object-relational database management system. MySQL is not extensible and does not provide the Data Domain Object. PostgresSQL is highly extensible and provides the Data Domain Object.
Yes, PostgreSQL is free, and code is available to use for everyone. It allows users to do anything they want with the code, including reselling binaries without the source code; thus, its free for all users, both proprietary and open source.