Basically, SQL stands for Structured Query Language which is basically a language used by databases. This language allows to handle the information using tables and shows a language to query these tables and other objects related (views, functions, procedures, etc.). Most of the databases like SQL Server, Oracle, PostgreSQL, MySQL, MariaDB handle this language (with some extensions and variations) to handle the data.
MySQL is a Relational Database Management System (RDBMS) that uses Structured Query Language (SQL). It is also free and open source and is commonly used with programs developed in PHP.