They can be tamed, but it takes a LOT of work. Basically, you need to handle them all the time from the moment they hatch. I never spent that much time with mine. I was content to let them be living decorations that make pleasant sounds.
Button quail are native to southeast Asia, so they do not tolerate cold nearly as well as coturnix do. That's the main difference in care that I can think of. They are much, much smaller, which you already know.