The two categories of X-ray anodes are stationary and rotating. As you might guess from the names, the main difference here is that one anode stays still (stationary) while the other spins around a fixed point (rotating).
The reason behind the introduction of rotating anodes is related to the dispersal of heat. All that energy coming to the anode from the cathode produces a huge amount of heat. If that heat keeps hitting the same spot over and over again, as in a stationary anode tube, eventually the surface of the anode can deform and the angle of the X-ray beam will shift, reducing dose efficiency and the overall image quality the tube is capable of producing.
In the case of a rotating anode tube, the heat of the incoming cathode beam is dispersed evenly across the entire surface of the anode as it rotates. This enables rotating anode users to perform longer scans and at higher doses.