The confusion extends to 28 inch wheels as well.700 x 38c tires often have markings that read 28 X 1 5/8.
A couple of weeks ago, guy wheels a dutch bike into the shop with a couple of brand new tires hung from the handlebar, asking if we can install them for him. Without even looking at the sidewall of his existing tires, I told him his new Continentals were not going to fit.
622 tires will never fit on 635 rims.