Obviously, client-side prepared statements are statements that are prepared by the client, rather than the server.
PDO is a data-access abstraction layer that supports multiple DBMS interfaces (drivers), some of which support server-side prepared statements (e.g.: MySQL 4.1+), some of which don't (e.g.: MySQL 3).
In the event where the PDO driver does not support server-side prepared statements, PDO will emulate them on the client-side and use the generic query interface to execute them.
The reason why MySQLi doesn't support them is simple: MySQLi is a MySQL-specific extension, a RDBMS that indeed supports server-side prepared statements, so there is no reason to emulate them.
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