The West and Christendom are related but separate concepts, and they have messy and vague identities. Christendom is the Christian world, specifically the Catholic world and protestant countries which were formally Catholic. It arguably does not exist now and was even in the middle ages, more of an ideal than anything. Which probably reached its zenith with the Crusades. It didn't include Byzantium, what remained of Al-Andalus or the Eastern Orthodox World, much less the pagan remnants in Eastern Europe.
The West is far more nebulous-it incorporates Christendom, it also incorporates the European settler colonies, at least the United States, Canada, and Australia and New Zealand. This grouping alongside the UK form something within the West called the Anglosphere. Something which was seen as distinct even at the beginning of the century from Germanic Civilization-witness the animus both the French and Germans had towards the commercialized, crass and perfidious Anglo Saxons. You might argue the West in the 20th century before the Cold War was subdivided between Anglodom, Francodom, and Germandom. With Slavdom being seen even in 1914 as something distinct from the West.
Most broadly there is the idea of a pan Western Imperium, or more bluntly a White world-which incorporates, both the smallest European enclaves left in Africa, the Settler colonies, and Europe itself. Basically the entire White world in a racial sense. Though that was historically divided, often by Nordicists, that of course emphasized Germany and Northern European superiority over the Slavs, decadent Latins and crass Anglo Saxons.
For a long time, Byzantium and the Eastern Roman Empire was not seen as part of the West either, the Latins in the 4th crusade, but historically and culturally are now.
In more recent terms, the West was Anti Communist or Anti Soviet, and was also in general set against the Communist or Bolshevik East, the USSR, China, and their satellites. Even the Western left was quite culturally distinct from its fellow travelers across the Iron Curtain.
At its further broad, even broader than the crude "Where White people live", the West incorporates Latin America, a region long peripheral to Europe and North America, but also still resolutely Christian, and heirs at least in part to the Spanish colonial legacy, as much the preceding Amerindian cultures. In some places though-such as the Afro Caribbean, a cultural sphere, the notion it is part of the West seems rather questionable to me. I suppose you could say certain places in the Caribbean or Latin america are peripheries on the periphery.
Haiti too, you could argue some of the African dominated Caribbean islands are an extension of African civilization.
In modern terms the West also incorporated the First World, that is the capitalist world, opposed to the communist one-more than a few Asian states, that were US aligned(or more bluntly American vassals), against Sovietism. These I do not think can be seen as "Western" in spite of their recent historical and economical alignment with the US.
I would say the West can at its most broad, can be used to incorporate all of these sub categories, or if you wish to be less broad in your classification remove this or that part from its sphere, depending on your preference? Korea and Japan are not majority Christian, their just aligned in recent history with the US and hold to the Capitalist economic principles.
TLDR: The West has multiple sub cultural spheres that overlap but still retain great cultural and historical differences, and a good argument can be made some elements of the West are not really Western, but are merely American vassals.
@Skallagrim your thoughts on the above.
