>>6487622As somebody whose being doing some research of the subject, I'd say there's actually a lot more types:
Chief resource:
https://en.wikipedia.org/wiki/List_of_one-eyed_creatures_in_mythology_and_fictionNote that, while there are many, I shall go by those that are humanoid/human-ish, hence the term monoeye.
~
Cyclops - Primordial mono-eyes from Greek mythology. Aside from the notorious Polyphemus, the Greeks also note three titanic cyclops who were Uranus's children, and who also were great smiths. Zeu's lightning bolts, Hades's helmet, and the like, were all their creation.
Arimaspi - A legendary race of Scythian monoeyes who fought with griffins
Hitosume-no-kuydo and Hittotsume-no-kozo - The one eyed children and monks. Also the possible soruce of the monoeye fascination in Japan
Its kinda late, so I'll have to work on this a bit more later.