Unlike most things, a chair's height, at least where I am from, usually refers to the seating position, not the top of the backrest. Of course, this is probably mostly a contextual thing. At some restaurants, bar stools and certain chairs are much taller than other chairs in the same restaurant. I used to struggle to get in the tall ones when I was a little kid. We discussed tall and short chairs a few times because of this.
Funny, I completely forgot about this until you commented.