Basically there are some major differences:

1. mysql_pconnect creates a 'persistent' connection therefore the link to the database is always open, mysql_connect however isnt like that and its links are closed when the script finishes and therefore must be reopened.
2. mysql_pconnect searches for exisiting persistent connections ans re-uses them if they are found, mysql_connect on the other hand, does not.
3. Links created with mysql_pconnect cannot be closed with mysql_close

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mysql> SELECT * FROM `users` WHERE `users`.`clue` > 0;
Empty set (0.00 sec)