"Western" is reserved for North and South America since it is "west" of the Atlantic. Eastern would be China, Japan, India, etc.
"Western" is a euphemism for ethnically European.
It is quite distinct from the "western hemisphere", which is a euphemism for the Americas. Technically speaking, parts of Europe and Africa are in the western hemisphere, as well as part of Russia and some Pacific islands, but when people say "the western hemisphere", that's not what they mean.