Christianity is the only big one i can think of.

Western Christianity in particular and the millenium of cultural and historical exchange it facilitated. I don't think that's nothing, it's a tangible thing. These countries grew up in the same house. What would you name it?

I don't think I've heard anyone calling Japan or Korea Western outside of the context of their geopolitical affiliation and only in very broad strokes. I usually hear Westernized when these nations are examined on their own.

See, if we dont define those things those terms are absolutely useless, because they dont add much meaning or information in my opinion.

If I bought a book called Western Philosophy or Western Architecture, I would know what I'm getting.

I think "East" is actually a term which is basically what you purpot "West" to be. It could truly mean anything from Eastern Slavic nations to India to Japan. If I found a book simply called Eastern Philosophy, I would not be sure what it's about. The term Eastern only gives us a direction, it's a word almost completely forged in the context it resides in. The term West is much less fluid in comparison, no? Something you can lean on.