How are korea's history and culture linked to those of china and japan?

Because of the goverments and thing that take place.

I believe that Korea maintained a separate and unique culture.

Whereas Japan and China are intermingled, with Japan having taken a lot of Chinese culture and adapted it as its own, Korea managed not to give in to outside influences. Japan took the writing system (kanji) from China, as well as many other cultural aspects - however, Korea remained isolated, especially in the context of Asian cultures.