Say you are riding on 622-19 rims. This means that each rim's bead diameter is 622 mm, and the distance between the two beads on each rim is 19 mm.
ETRTO stands for European Tire and Rim Technical Organization. But that does not mean that if you are riding, say, 25 mm tyres, you can refer to your tyres as 622-25; does it? Can the smaller/second number refer to the tyre width, so that you would say "I installed 622-25 tyres on 622-19 rims")?
Also, I see 37-622 in addition to the more common 622-37. Which one is correct?