MYSQLI is going to become the new standard in the next couple of years. Most of the functionality is the same, but the connection to the database and the method in which you execute queries is somewhat different. MYSQLI boasts significant performance improvements over the standard MYSQL. For clarity, MYSQLI is more of a reference to how you interface with the db... it's still a MYSQL database platform.

If possible, I would be sure to consult sources that reference MYSQLI. MYSQLI is supported in PHP 5+, so don't expect to get much practice on a server with a version lower than that installed (most run PHP 4).