SQL stands for Structured Query Language, and it is a programming language designed for querying data from a database. MySQL is a relational database management system, which is a completely different thing.
MySQL is an open-source platform that uses SQL, just like MSSQL, which is Microsoft's product (not open-source) that uses SQL for database management.
SQL - Structured Query Language. It is declarative computer language aimed at querying relational databases.
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.
SQL stands for Structured Query Language, and is the basis for which all Relational Database Management Systems allow the user to add, remove, update, or select records. Things like MySQ are the actual Management Systems which allow you to store and retrieve your data, whereas SQL is the actual language to do so.
The basic SQL is somewhat universal - Selects usually look the same, Inserts, Updates, Deletes, etc. Once you get beyond the basics, the commands and abilities of your individual Databases vary, and this is where you get people who are Oracle experts, MySQL, SQL Server, etc.
Basically, MySQL is one of many books holding everything, and SQL is how you go about reading that book.
SQL is the actual language that as defined by the ISO and ANSI. Here is a link to the Wikipedia article. MySQL is a specific implementation of this standard. I believe Oracle bought the company that originally developed MySQL. Other companies also have their own implementations of the SQL standard.
SQL is Structured Query Language
MySQL is a relational database management system. You can submit SQL queries to the MySQL database to store, retrieve, modify or delete data.
Source: Stackoverflow.com