In the east a lot of furniture is very low or even on the floor itself, for example, shikibuton, tatami, etc. Why the big difference in height?
Your question is based on an illusion, and a degree of wall-building that you seem to have clear in your mind but that is a mystery to me.
Right now, your definition of "the east" seems to be only Japan, ignoring mainland East Asia, southeast Asia, the Indian subcontinent, and everything until you hit, what, the Greek peninsula?
Traditional Japan is an outlier in its dislike of raised seating. BTW, tatami is not furniture. It is flooring, like shag carpet is.
China, on the other wing, developed a beautiful array of forms of chairs, stools, benches, and sprawling couches, besides raised beds. To go with this they had scroll tables and writing desks, dining tables and others for all occasions. All heightened from the floor.
This actually influenced European furniture. When we escape Jacobean spindle turning, part of the influence on Queen Anne styles was Chinese. If you look at the brass plates behind drawer handles, you will see that they are the traditional Chinese bat. But the Europeans turned them upside down, like they threw away tea water at first and tried to eat the tea leaves like boiled greens. Things were twisted in translation.
Often, to have furniture or not has less to do with where you are and more to do with your status in your culture. A poor farmer might have a bed like a packing crate with mattress and curtains, and maybe no curtains, while the wealthy had carved teak or rosewood or sandalwood fretwork surrounds for their beds with silk-noil-stuffed mattresses and curtains whose weight was changed with the season. The farmer would have a bench and some stools, all hard and backless, while the rich had arm chairs with cushions. You can see this divide applies in Europe and China, both.
In many places the poor sit on mats on the floor, not because their culture lacks the idea of raised furniture, but because it's out of their league.
Even in places without easy to move chairs, sitting is done on divans and benches, often built in to the architecture. If you are making an adobe cottage, you might as well build in an adobe bench. In "the west", when chairs were uncommon in the Middle Ages, chests would be utilized for seating, to the point that some had skeletal back support.
Of course, nomads often skip furniture as unnecessary weight. They are often ground dwellers.
Working on the ground, or very short seats, is often part of a craft. Metalworkers or woodcarvers don't need special clamps with padded jaws when they can hold the work in their feet.
I am on phone, not able to access library until later. I will recommend looking up Chinese Furniture in Measured Drawings to see some of the variety of chairs and tables.