that has nothing to do with metric vs imperial:

"Lumber manufacturers typically cut a tree into the various standard types of dimensional lumber very shortly after the tree is felled. At this point, the 2 x 4 is actually 2 inches x 4 inches, a 2 x 10 is actually 2 inches x 10 inches, etc. But then the newly-sawn (but soaking wet) lumber is then kiln-dried until it reaches the desired moisture level. During this process, it shrinks as the moisture in the wood is removed and the wood cells shrink. Once the drying is complete, the boards are then planed to a standard size. Hence, what started out as a 2 x 4 now measures 1 1/2 inches x 3 1/2 inches."

https://www.thesprucecrafts.com/why-isnt-a-2x4-a-2x4-3970461