I would love to go mountaineering.  A trip to Mount Kailash in Tibet is on my bucket list.
Seems too dangerous to me. Although the term can be related to backpacking, hiking, skiing and any other outdoor climbing.
LOL. No one can climb Mount Kailash. it is a holy mountain.  You circumambulate , or walk around the mountain.
I don't know much about it. Mountaineering started out as trying to reach the very top, but now it has other aspects that people aspire too.
i don't see how some of them do it.  having to breath from an oxygen bottle and losing fingers and toes to frostbite.
It takes a lot of skill and ability plus knowledge of safety to be able to do what they do.
Isn't it expensive to climb the major mountains, like Mount Everest?
I wouldn't think it would cost money to climb mountains. Sometimes it is called Alpinism, more common in European languages, where you climb with little equipment in snow and ice.