Polyurethane is a general classification of plastic which Polyether and Polyester belong to. We industry folk tend to speak of polyurethane because both polyether and polyester are/can be used in the same family of boots depending on which characteristics are needed.
Polyether and Polyester are both top level plastics, but you will see more polyether boots on the market. Polyether is much clearer so when you see a boot with a high level of transparency, it is most likely polyether. Polyester tends to be a bit milky in color, so that tends to be reserved for solid colored boots. If a boot is solid in color it could be either of the two but if a boot is fully transparent or transparent red or transparent blue etc, then it is most likely polyether.