A breakout board facilitates connecting your drives and other devices to the parallel port pins. The parallel port is sending the step and direction signals to the drive.
With a motion controller, the motion controller generates the step and direction signals itself, based on commands that Mach3 sends to it.
A Smoothstepper is a motion controller. When you add a Smoothstepper to a PMDX 126, you have a breakout board with a motion controller mounted to it.