Actually out of curiosity, I'd love to hear a Japanese or Korean persons take on this claim. Im from the Middle East so Syria and France seem pretty different for me, but maybe if you're from the country/region being compared it's a lot easier to see the differences.
My background: citizen of USA, son of two immigrants from Korea. Hopefully someone who actually lives in South Korea or Japan can step in here too.
Subjectively, it seems to me like Japan and South Korea are somewhat culturally similar, but they are not the same, and the differences are important to people there. Furthermore, 20th century history has created a lot of hatred on both sides. These wounds are starting to heal with time and _I think_ the younger generation in Korea tends to care less about the issue. Many people in both countries go to the other country for tourism, and each country's cultural exports are popular in the other country.
For an analogy (though not a close analogy, because the political situation is different): Israel and Syria are pretty similar though, right? Both speak Semitic languages, they have similar food, similar weather, similar religions, and often you can't tell them apart just by looking at them. So they should be friends. :)