Why Korean and Japanese are Similar to Each Other

The main reason why Japanese and Korean are similar is because of the ties between Baekche and Japan until the combined Silla and Tang Chinese forces defeat it circa 7th century CE.

Then all the Baekche royalty beat it to Japan, where their colony had grown into a distinct country through interaction with Okinawans (they kept the Koreans and proto Japanese at bay off Kyushu) and the Ainumushiri.

It was the Ainu whose language influenced and shaped Japanese vocabulary, because the people of Wa needed women to propagate the species.

So when a Japanese is taught he is "descended from the gods", it means he is heir to Baekche and mainly Korean ancestry.

After 700 CE, Korean had Chinese loanwords absorbed into their language due to Tang influence.