Seoul a city, state or both? Which is it?

Seoul a city, state or both? Which is it?
It's neither one of it.....In fact
Seoul (서울) is the capital city of South Korea. And it is divided into 25-gu (구), or districts / in Mandarin it is referred as 区 (qū).

Seoul, together with the surrounding Province of Gyeonggi-do (경기도) and the Special City of Incheon, makes up the Seoul National Capital Area (수도권).

25-gu (districts) of Seoul

From Jung-gu (the smallest) to Seochu-gu (the largest), Seoul boasts 25 districts over 605 km².

For more info about Seoul: WIKI