SQL is the language, and a set of standards define several levels of it.
Various database products implement different levels of SQL.
MySQL is an open source (free for non-commercial use), very rapidly developing, database management system. There's a whole constellation of software companies that publish gui's and other things you can use with MySQL, in addition to the ones which MySQL itself offers. Some people ( the folks who don't know about TOAD for MySQL ) even use Access as a front end gui for MySQL.
Access is sort of like a "pain (t)-by-the-numbers thing with training wheels on it. And it marries you to Microsoft and it's not free like MySQL.
EG: Access would be used by a person working alone or in a small office workgroup, say 5 people or so. MySQL can do that too, but can also support huge databases and lots of users, say maybe an entire corporation with thousands of users. Something like Oracle would be even bigger-gun stuff.
There are lots of competing RDBMS systems. I don't recommend messing around with Access. MySQL is a good way to go.