I figured since they share a land mass they must have been one people at one time if you go back far enough. I bet they were... possibly before a written record has been kept.
Linguistically they are very distinct.
Korean is actually very weird.
Korean is so different from Chinese and nearby languages that it constitutes its own language family, an isolate with only very tenuous connections to any other. One theory for instance connects it with Dravidian languages (Tamil, etc.) of Southern India. Thats how far people have looked.