Emperor
Je (제; 帝), or emperor, existed for less than two decades during the Korean Empire.
King
Wang (Han-geul: 왕; Hanja: 王), or king, was a title used in Goguryeo from 37 BC to 668, in Silla from 500 to 935, in Baekje from 18 BC to 660, and in Goryeo from 1274 - 1392. In early Goryeo (918 - 1274) and the entire Joseon Dynasty (1392-1910), the rulers of Korea were still known as "kings", as evident in the title title of King Sejong the Great, 世宗大王. However, they were referred to by their temple names.
Some kings have the title of Maripgan
More names, see Rulers of Korea.
Gun
Gun (군; 君) is sometimes translated as "prince", but may be the ruler of a kingdom as well.