Koreans make a great deal out of having an equalitarian society (in terms of hereditary class).
To say the least the Korean people were "divided" when it came to the Japanese occupation, as were the Japanese themselves about Korea.
And no, they are not the same people. 40% of modern Japanese have a tooth type found only among the ancient Jomon and present day Ainu. The Shan Dynasty Chinese who fled Shan at the start of one or the other of our various Dark Ages who ended up in Korea on the South Coast moved on to Japan quite early and never mixed cultures with the later Mongol arrivals to Korea.
The Japanese royal family was recently found to descend from Korean invaders from the 500s.
It gets quite complex from there, but the two nations are more different than they are alike. There have also been many centuries of voluntary immigration into Japan from Korea. Japanese fishermen certainly established small villages on the coast of Korea. Both nations also went through periods of total rejection of the outside world with bouts of what can only be called "ethnic cleansing".
Politically, claims that both nations use cognate languages are considered a legacy of the Japanese militarist's excuses for the conquest of Korea. In reality, there are similarities - mostly in terms of vocabulary, like English and French, but the Polynesian grammatical elements in Japanese have no equivalent in Korean. In time English will supplant both languages, albeit an English without an "L" sound!
Still, you have to remember Mr. Rhee got started in 1897 demonstrating against YI. One doubts that he ever really changed his mind.