Japanese and Korean are a hell of a lot more similar to each other than either is to Chinese. They both have similar grammar, while Chinese grammar is way different, borderline nonexistent, in my opinion.
I wouldn't call it nonexistent just because it's analytic. I always thought of such languages as having simpler morphology (or in the case of Chinese, none) and more complex syntax. A language like Latin has complicated inflectional paradigms but virtually free word order.
Some scholars actually classify the Japonic & Korean languages under Altaic, but this is not widely accepted. Korean classification is still ongoing, though, & it may end up in the Altaic group after all.
I'm skeptical. The Uralic and Altaic families were once thought to be related due to similar structural features (SOV word order, agglutination, vowel harmony) and it was found those resemblances were areal, not genetic. I suspect it's the same for Japanese and Korean which have been spoken in the same area long enough for a sprachbund to develop.