You may notice the term "Nominal Size" and "Finished Size" for most goods. In the example of 2x4 timber, 2x4 refers to the "Nominal Size". This is the rough-sawn size of the timber before machining or regularising. The reason for this difference comes from wood being a natural product. Not all timber is going to dry to the exact same size, so if left as a full 50mm x 100mm it can lose up to 2mm on each dimension during the drying process, but this number varies.
To make life simple, some timbers such as Carcassing are machined to a "Finished Size". This makes the common 2x4 (or 4x2) an industry standard size, allowing architects, builders, carpenters, etc plan in accordance with these known sizes, rather than working from variations or rough dimensions. This simplifies the process and makes life for everyone involved easier.
So what size is a 2x4 (or 4x2)? When looking at Carcassing (for example our 47mm x 100mm C24) has a finished size of 45mm x 95mm, or in imperial 1.77 inches (1 49/64) x 3.74 Inches (3 47/64). Rounded for simplicity this equals 1 3/4" x 3 3/4", so your standard 2x4 (or 4x2) actually runs on average 1/4 inch undersized.
If a final dimension is critical, always measure in Metric using the Finished Sizes as your reference!