SQL (Structured Query Language) is used to perform operations on the records stored in database such as updating records, deleting records, creating and modifying tables, views etc.
SQL is just a query language, it is not a database. To perform SQL queries, you need to install any database for example Oracle, MySQL, MongoDB, PostGre SQL, SQL Server, DB2 etc.
MySQL is a relational database - a piece of software optimized for data storage and retrieval. There are many such databases - Oracle, Microsoft SQL Server, SQLite and many others are examples of such. The MySQL development project has made its source code available under the terms of the GNU General Public License, as well as under a variety of proprietary agreements. MySQL was owned and sponsored by a single for-profit firm, the Swedish company MySQL AB, now owned by Oracle Corporation.