MariaDB is a binary drop-in replacement for MySQL, created by some of the original MySQL developers including Monty Widenius. According to Monty, there is no reason to use MySQL as "MariaDB is faster and has less bugs".
Licensing can be a bit tricky for MySQL and MariaDB because of their use of the GNU General Public License version 2. You probably want to read this Licensing FAQ by Monty Widenius.