None of the above is true, or at least isn't the full answer for why today a "2x4" is missing an entire half an inch all the way around. The shrinkage due to drying is around 5% (and the real math there is more complicated, as wood shrinks different amounts in different directions relative to the grain), which would only account for 1/10" of difference in the thickness of a 2x4. With some species of pine it's as low as 2%.

No, the lumber industry has consistently shaved boards in order to fit more into rail cars for transport and make more money and spend less per plank on transportation costs. Various lumber consortiums determined via internal testing that the smaller board sizes are still "sufficient" for their intended purpose vis-a-vis structural integrity of stick framed residential buildings.

Wood does shrink while it dries, and that is the reason why a "2x4" is actually 1.5x3.5, but you're missing a lot of detail in there.

To make a tree into boards, first a lumberjack fells the tree and bucks off the branches. It is then taken to a sawmill where a big clumsy saw slices it into kind of rectangular shapes. I will gloss over some nuance here about the algorithm chosen to do that and how it relates to the growth rings to produce boards of different qualities. You now have green boards, VERY wet. If you were to build something from these boards, as they dried they would warp and twist and pull the assembly apart. So it has to be dried.

At commercial scale, this is done by stacking the boards with spacers in between so air can circulate through the pile and letting it sit outside for a few months, and then the piles are taken into a kiln and heated for a couple weeks. The weight of the stack, or perhaps straps holding the stack together, has kept the boards relatively straight, but they will have warped a little. Before they're used for much, they have to be more precisely cut so they are straight, square and true.

Woodworkers making fine furniture tend to buy their lumber rough cut and mill it themselves, so that the lumber is as flat, straight and square as possible. Let all warping happen while the board is rough and mill it as a first step in building so that the pieces are very precise, and then the finished assembly holds itself true. Woodworkers buy wood per unit volume; it's usually priced per board foot. A board foot is 1 foot long, 1 foot wide and 1 inch thick, or 144 cubic inches. A 1 inch thick, 6 inch wide, 8 foot long board is 4 board feet. Checking out at the lumber yard requires a bit of middle school geometry homework.

Carpenters building houses or sheds used to do the same. In the early 20th century, lumber companies shipping lumber long distances by rail started shipping wood pre-milled. It doesn't really matter if the boards are a little warped; the worst boards in a stack can be cut into the smaller pieces you need, the better ones used whole for studs or plates. Pre-milling the boards at the sawmill means that it's cheaper and more efficient to ship the lumber, the sawmill now has the sawdust/shavings/chips to make particle board, OSB and other engineered lumber products out of, and the carpenter gets a commodity product he can buy and use rather than a raw material that needs further processing. Because they're all the same size, they're sold at a price each. It was a true 2 inches by 4 inches in the kiln, and the milling has been done for you.

I don't think this is true. There was a transitional period around the 1940s where 2x4s were 1.75" x 3.75", and that wasn't because wood shrunk half as much as it does today.

that's one of the common excuses that the mills quote. It's bullshit of course, but it sounds plausible so they continue to get away with it.

Another bullshit excuse is that they're providing an additional service by milling and planing the lumber for you, and that the nominal measurement is before that process.

It's all just greed. If they could get away with selling a 2x4 that was half an inch thick, they would. At least it's all standardized now.

Unfinished 2x4s are actually 2in x 4in, which originally you would trim on all sides to get a nicer surface getting down to the "modern" dimensions. Nowadays, you pretty much only see pre-trimmed lumber.

There is no sensible reason to sell something as a dimension before it's ready to sell, a 2"x4" should be so when sold, not when curing, it takes nothing to cut oversize to accomodate for shrinkage, or to cure and cut later at the right dimension

Modern lumber is planed, so some of that difference is because of losses from that. If you open up the walls of a house built 100+ years ago, you see these thick rough wall studs that never went through a planer. Even with shrinking, it's close to being actual 2" x 4".