Not at all. mysql_connect is a function (commands are what you execute at prompt to tell a computer what to do) belonging to the mysql extension. mysqli is another (newer) improved mysql extension which offers both a procedural and object oriented interface.
PDO is different in that it offers an object oriented interface to a variety of database drivers (including MySql).
I have seen some of your code and would not call it OOP. You use classes and objects yes, but are not designing around OOP design patterns. Having said that, if its OOP you want to get into (and even if its not), PDO is probably a good option. While it doesn't (by itself) provide a complete abstraction from different database implimentations, it can get you a good part of the way there.