The characters 宗 (종) and 祖 (조) were titles of honor for Korean kings, but the character 君 was used for kings who had been dethroned and denoted back down to prince for dishonoring the throne. Though 宗 (종) and 祖 (조) were titles of honor, they were not of equal honor. The character 宗 (종) was attached to the names of kings judged to have been "virtuous," and the character 祖 (조) was attached to the names of kings judged to have been "meritorious." A "virtuous king" simply fulfilled his expected duties as king, but a "meritorious king" did something beyond his regular duties that earned him special merit, suggesting that kings with names ending in 조 were a step above those with names ending in 종.
The following is a list of the Korean pronunciations of the first characters used for the twenty-seven names of the Joseon Dynasty kings. It might help you memorize the order.
정순헌철 고순After memorizing the list, then you just need to learn on which names to attach 종 (宗), 조 (祖), or 군 (君).
The first king of the Joseon Dynasty was King Taejo (太祖). The attached 祖 means he was considered a "meritorious king." Apparently establishing a new dynasty was quite a feat, earning him his special merit. The character 太 (태) means "great," and was the same character used for the founder of the Goryeo Dynasty, whose name was also "Taejo" (太祖).
The next Joseon Dynasty king to have 祖 attached to his name was King Sejo (1455 - 1468), the seventh king of the Joseon Dynasty and second son of King Sejong the Great (1418 - 1450). The first son of King Sejong was King Munjong (1450 - 1452), who died shortly after becoming king, passing the throne to his 12-year-old son, King Danjong (1452 - 1455). Though King Sejo had forced his young nephew to abdicate the throne to him and killed many people, including his nephew and younger brother; King Sejo apparently earned enough merit by strengthening the monarchy and improving government administration to have 祖 posthumously attached to his name.
Even though King Sejo demoted King Danjong to prince, thereby, reducing his title to 君 (노산군), he is now referred to as King Danjong because scholars during the reign of King Sukjong (1674 - 1720) felt that he had been undeservingly dethroned and, therefore, they restored his title and gave him the posthumous name "King Danjong."
Anyway, the point I want to make is that even though King Sejong the Great is now credited with many achievements, apparently none were considered great enough at the time to merit 祖 being posthumously attached to his name. I find that somewhat interesting.