It’s not even approximate. A typical two by four is around 1.5 by 3.5 inches, which is a full third less material than lumber which literally measures 2 by 4.

IIRC this is because "two by four" refers to the size of the rough-sawn stock, but you buy milled 2x4s, so the difference is simply what's removed in milling. You can get these odd formats (stuff like "78x34 mm") in hardware stores here, too, it's just that they're not used for construction, because construction lumber is "hard metric", i.e. nice round numbers like 40x60 mm etc.