Within the British Isles, Scottish and English are supposedly distinct ethnicities. How well can you tell this from still photographs devoid of cultural cues? Not very. Are there distinct gene pools? According to the documentary, "A Celtic History of the British Isles," not so much. Basically, there was so much interbreeding under the Romans, there's hardly any genetic distinction left.

I'd expect there to be some small degree of genetic distinctness, but there has always been a history of interbreeding. There's even an old Korean stereotype about rich bewhiskered Chinese merchants who come down to marry a hot young Korean wife.

In short -- Ethnic differences between Han Chinese and Koreans: mainly cultural.