A Japanese style bed is called a Futon.
A Futon which is a Japanese style bed consists of a mattress (敷き布団, shikibuton, lit. "spreading futon") and a duvet (掛け布団, kakebuton, lit.
You can buy futons in the USA as well but I find them very uncomfortable to sleep on.
I had a futon in college and could feel the metal in the futon under the very thin mattress and I found it much more comfortable to sleep on the floor instead.
However maybe the actual Japanese Style Bed Futons are more comfortable and it could just be the USA sold ones.
But I would rather sleep on the floor.
Also some Japanese people do sleep on the floor or just on a small mattress on the floor as well.