East Asia since 1868
When the samurai era ended in 1868 through a civil war, Japan started to fully open the nation to the world and modernize and westernize the nation.
Subsequently Japanese succeeded in its own industrial revolution to build up strong military forces. But at the time Japan was threatened by the Russian Empire coming down to the south through Siberia.
Other western powers, including the UK which defeated China in the Opium War (1842) and the US which compelled samurai Japan to have a diplomatic tie with the US, also forced Japan to accept unequal treaties (1854). Japan could not, of course, rely on these western colonizing powers to take preventive measures against the imminent threat from Russians. Japan had to rely on its inherent samurai (warrior) spirit.
On the other hand, the Korean Kingdom was still in its seclusion policy like samurai-era Japan. Koreans were desperately split between farmers and noble men. The rotten Korean court was unable to boost its economy and enrich the nation. Korean farmers were left in a state of illiteracy and ignorance mostly due to the discriminatory social system of Korea built on extreme Confucianism. It was apparent that Korea could not modernize and westernize itself. What is worse, Korea nominally belonged to China. Corrupt Yi-Dynasty Korea was a tributary to more corrupt Ching Dynasty of China. And Ching itself could not modernize itself even after the defeat by the UK in the Opium War.
So, when Japan put an end to the rule by sword of samurai in 1868, East Asia was, like South East Asia and South Asia, about to be directly and indirectly colonized by the UK, France, Germany, the US, etc. What is worse, the Russian Empire was for real trying to move its mighty troops from Siberia into Manchuria and North Korea. But Ching Dynasty and Yi-Dynasty Korea could not stop this military invasion as they had no strong military and modern industry. They could not carry out their own industrial revolution.
At the time leaders of the Empire of Japan thought that it was a matter of time that strong and modern Russian troops would occupy Manchuria, part of northeast China, the Korean Peninsula, and then eventually the Japanese Archipelago. Tokyo had to do something to prepare for a coming showdown with the Russian Empire.
As the first step, Tokyo tried to educate Koreans so that they would sever its centuries-long subordinate relationship with China and get fully independent. Japanese politicians expected that new Korea would join Japanese efforts to keep independence of East Asia from western powers and Russians. But as Korea's old tie with Ching was so strong that the Empire of Japan had to make a war against Ching China to free Koreans from the Chinese rule. This is the First Japanese-Sino War which was fought from 1894 to 1895.
The defeat of Ching Dynasty eventually led to its all-out fall in 1912. But Korea could not advance its society all by itself after the war, so that the Korean Kingdom was eventually fully annexed to the Empire of Japan in 1910 (though some Japanese leaders were against this measure imposing a heavy financial burden on Tokyo). And most importantly the Empire of Japan fought the Empire of Russia between 1904 and 1905, extensively using its military bases in the Korean Peninsula built after the First Japanese-Sino War. The victory of the Empire of Japan over the Russian Empire took away the threat of brutal invasion and inhuman colonization by Russians from East Asia.
This is the basics for understanding current situations and relationships among Japan, South/North Koreas, and China as well as Taiwan and Mongolia.
Indeed the 21st century is based on the 20th century which was a kind of extension of the 19th century and preceding centuries.
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Mat 8:15 And he touched her hand, and the fever left her: and she arose, and ministered unto them.