MySQL is a relational database management system (or RDBMS) –meaning that it is a database management system based on the relational model. This RDMS runs as its own server and provides multi-user access to multiple databases at once. The source code of MySQL is available under the terms set forth in the GNU General Public License as well as a plethora of proprietary agreements. Members of the MySQL community have created many different branches of the RDMS –the most popular of which are Drizzle and MariaDB. As well as being the prototype of several branches, most free software projects that must have a full featured database management system (or DMS) use MySQL.
MySQLi Extension (or simply known as MySQL Improved or MySQLi) is a relational database driver that is used mainly in the PHP programming language. It provides an interface to the already founded MySQL databases. It is quite literally an improved version of its predecessor, MySQL, which was simply a means to manage databases over servers.