The Greek word meant "alone". Thus an oligarch rules in company with a small group of other people, but a monarch rules alone.

Internal to Greek, mon- was the conventional prefix for a meaning of "one", despite the word for "one" being different. This didn't happen in Latin, where the numeric prefix uni- ["one"] derives from unus ["one"] and not from solus ["alone"].

The Chinese terms have preserved a robust distinction between "one", the number, and "alone", the state of being. It's a strange choice, though, to offer different translations for the same concept in two closely related words. That distinction isn't in place in the original words.