The bridge (or Greinacher) type qualifies as a full wave voltage doubler. Also the Cockcroft-Walton type.
Full wave refers to the fact that the load capacitor receives a charge during both the positive and negative halves of the AC supply cycle. Hence this excludes the Villard doubler.
Full-wave has less ripple voltage than half-wave.
Full-wave requires more components than half-wave.
I have a Youtube video which is an animated simulation of the Greinacher voltage doubler. It portrays capacitors charging and discharging. It portrays current bundles moving through wires.