MySQL and MariaDB are two different free and open source database programs that are compatible with each other. Any program that requires MySQL will also run on MariaDB and vice versa.
May First follows the decision of the Debian project, which has chosen MariaDB.
MySQL was the original program developed by a Swedish company in the mid 1990's. It was later sold and now is owned by Oracle.
After selling MySQL, the original developer started MariaDB using the same code base (which has since diverged).
See the MySQL wikipedia page for more details.
See our help file on installing MySQL.