MySQL is a program that will host a database, allowing other programs to connect and read and/or modify the database.
SQL stands for "Structured Query Language". MySQL is a flavor of that language. Some instances of the language are as follows:
SELECT * FROM MyTable;
SELECT username, dateOfBirth FROM MyTable;
INSERT INTO MyTable (name, username) VALUES ("John Doe", jdoe97), ("Jane Doe", jannie_d);