Horde_Controller is the Horde 5 MVC Controller package.
Horde_Controller brings its own Request and Response classes which are neither compatible with Horde_Http nor with any external standards.
The Horde_Controller base classes are used by Horde_Core's RequestConfiguration. Nag uses these Controllers for saving tasks.
Horde 6 replaces Horde_Controller with Horde_Http_Server.