MySQL has been the default open source database for many years. Its part of the LAMP stack which is the most popular role for Linux web server appliances.
Microsoft has changed the database availability in 2016 so that even the F1 service (free) can now have a small 20MB database so that WordPress users like us can function. More store is available for a modest cost.
The MySQL is offered by ClearDB which itself is based on virtual machines in the Azure data centers. This is an example of a cloud business that does not own any of its own servers.
The MySQL database is available with more room for larger sites up to a maximum of 10GB. After that a virtual machine is recommended with MySQL running in stand-alone mod