MySQL

MySQL is a database system. It is one of the most widely used free and open-source databases. PostgreSQL is preferred by many nowadays for political but also technical reasons.

OpenStreetMap swapped from using MySQL to PostgreSQL for its main Database around 2009. For a while, The Rails Port code could still work with MySQL. However, this is no longer the case (at least not without a lot of hacking).

Of course, there's nothing to stop developers from working with OSM data and MySQL.