It reminded me of a story on Reddit recently about a couple who adopted an Asian baby and then raised him diligently and positively introducing him to Chinese culture, language classes, special efforts with food and communities, etc so he didn't lose that part of his background. At around 18 years of age after almost two decades of efforts along these lines, the father discovers the kid is actually Korean and can't bring himself to tell his oblivious son or wife!
Reminds me of a friend's anecdote about people in Scotland in the 60's talking about differences in accents resulting from being from a town 9 miles away.
A lot of places in Europe are still like that. "In USA 100 years is a long time, in Europe 100km is a long distance"
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.
In this Reddit story, I think they did things like get him Mandarin lessons, practice various customs, find a Chinese "uncle and aunt" to take him to dim sum and whatever else. Then when signing his son up for college applications, the father noticed the surnames of his kid's birth parents were very typical Korean names. All those good intentions!