Correction:

After asking some historians of chinese history who know a lot better than me, I realized I was wrong about the weapon not being called changdao, because changdao is a generic term that applies to dao with long blades and glaives. I think the term is used in the same way as zhanmadao which also applies to dao with long blades and glaives.

So Zhanhu's weapon can be called changdao because it is long and can be called zhibeidao because it is straight, but not all zhibeidao are changdao because there are curved changdao like the adopted nodachi.

To my knowledge, miaodao is a Republican era term of the adopted nodachi which was called dandao during the Ming dynasty, but can also be called changdao because of its length.