Theme Engine / Override Themable Output - Drupal7?

PHP Template
TWO ways to theme

  |-> Templates
         Pass data to a template which is a PHP file mixed with markup and PHP print   statements  (___.tpl.php)
         or
         If the module provides a template (.tpl.php file), Copy the template to your theme directory.
         

  |-> Theme functions
        Pass data to a PHP function to wrap it in markup (theme_[themehookname])
        or
        In the module code, identify the theme or preprocess function that is generating the markup you want to change and copy the function to your theme's template.php