@thegame2008:
The different types of Yagi antenna exist to serve different purposes, for instance, to get a high forward gain, low front-to-back ratio, sharp beamwidth, horizontal or vertical polarization, high or low antenna input impedance,etc... Each type of director, reflector and driven element was designed to serve a specific target.
However, all of these Yagi antenna comply with the Yagi antenna principle that: Antenna elements must be arranged in the order of reflectors, driven element, directors and ony driven element is excited.
hope it helps