韩国 is the generic term for KOREA, it does represent South Korean, however, not just included South Korea.
Also, you failed to comprehend that Korean in Chinese does not necessarily come from South Korea (Which specifically mean South Korean Expat) because China have its own Korean race due to geographic proximity. In fact, there are 3 type of "Korean" in China,
1.) ethnic Korean with Chinese Citizenship
2.) ethnic Korean with South Korean Citizenships
3.) ethnic Korean with North Korean Citizenships
And only number 2 is South Korean. It is estimated there are only 250,000 South Korean national in China, mostly on Business visas. It was quoted in the Korean Article one of you guy posted.
That's why I said, you are clutching the last draw. But well, you believe in whatever you believe in, if that help you sleep better at night, you can say "Millions" of South Korean in China, you can even claim there are 50 millions South Korean in China, as I don't really care about the issue anyway.