[thaumasiotes]

If you're Korean, India is Western. They share "Buddhism", though generally not the same sect of Buddhism. They don't share a cultural tradition.

[virtualwhys]

Japan and China (in the past) have had a long monastic tradition. I assume it's the same for Korea.

Monasteries are most definitely not exclusive to the west.

[kijin]

IMO South Korea has been Westernized much more than Japan or China.

Even before South Korea came under U.S. influence, Buddhism in Korea has been weaker than in Japan for a long while because neo-Confucianism took over as the state ideology in the early 15th century. Neo-Confucianism emphasizes going out into the world and contributing to the public good, not withdrawing into a hermitage. Most of the great Buddhist monks that people remember are from before the switch. Buddhism was often actively suppressed, and tolerated at best, for the last 600 years.