SQL (Structured Query Language) is the standard language for communicating between or within databases. And as far as computers are concerned, databases are simply collections of data.
MySQL (usually pronounced “My Sequel”) is one of many programs designed to store and retrieve data within the database as efficiently as possible. It’s also the most popular, due to its compatibility with WordPress and other popular CMS software.
For the vast majority of web designers and developers out there, there’s no real need to learn how to actually write SQL directly. The software you use to build your site, be it WordPress, Drupal, Joomla, or something else, will communicate to the MySQL database for you.
Think of it as the inner workings of a computer. You don’t need to know how to build a computer or even how it works in order to use it, you only need to know how to use the keyboard and mouse.