Taps and dies are close enough. Geographics, demograghics and etymology stretch the meanings in many different ways. The quality of what you are using, especially taps and dies makes the most difference. When looking at the die referred to as a button die, it does look like a button to some degree. I can imagine if someone had used the many different types of dies available, or had the different dies available in their shop, then sending the apprentice to the tool room for the button die would be correct or at least avoid confusion. Threading larger bolts or round stock you may need to use something like these; https://www.ridgid.com/us/en/pipe-and-bolt-die-heads.
I needed to thread 1 1/4" X 20' HR with 6 inches of thread on one end and 18 inches on the other so I used what most would see as a pipe threader, with a bolt threading attachment. I threaded ove 100 pieces and I still have about 60' of 1 1/4" HR if someone has a project.
One thing I would like to point out, if your die isn't adjustable then using a piece of 10mm round would produce a standard thread, and if you're not meeting strict tolerances you're good. Even if the 10mm round is a little larger the die will remove the excess material, so you just need to work a little harder.
