If you ask a baker what protein does in dough, they'll tell you protein forms gluten, the stretchy web that's necessary for making bread (but a less desirable quality in things like cakes). Protein affects the amount of water that flour can absorb. It's thirsty. Dough made with high gluten flour will seem less wet than dough made from flour with a lower gluten content. This can be true even if the same brand of flour is used to make the same dough. While measuring errors are one common problem, even if the measuring is precise, doughs made from the same recipe can feel different. The reason being, protein levels can vary within the same brand of flour. Although usually the amount of protein is stated on the bag, the actual amount will fall within a range depending on the manufacturer's tolerances. Even a small variation in the amount of protein can produce very different outcomes. But how much difference could it make?
This test was easy. I started with four different types of flour in four bowls—100 grams each of bread flour, all-purpose flour, unbleached cake flour, and cake flour—and I added 90 grams of water to each bowl. The bleached cake flour (bottom left in photo above) looks thicker, but looks are deceiving. It wasn't thicker, it's just that the others were smoother. Bread flour, with the highest protein content, was the thickest dough. It was stirrable, but it started developing gluten right away. After a short rest, I could lift the whole clump of dough with the spoon.
All purpose flour was a little wetter, or less thick, if you prefer to think of it that way. It was much easier to stir, but started to develop gluten fairly quickly. After a short rest, I could pick up most of the dough ball on the spoon, but since it was looser and smoother, it flowed off the spoon.
Unbleached cake flour is new on the market; until recently, all cake flour was bleached. The unbleached cake flour is formulated to have the same protein content as the bleached cake flour, but without undergoing the chemical bleaching process. It was even looser than the all-purpose flour. There was less gluten development, so it fell off the spoon in ragged clumps. It's not as bright white, and there was some gluten development. Not nearly as much as the bread or all-purpose flours, but more than the bleached cake flour.
The bright white bleached cake flour, besides being the loosest, also resisted forming gluten, even after quite a long rest. I could pick up a spoon full of it, but it didn't hold together at all.
Using bleached cake flour in lieu of bread flour would be an extreme substitute, but even the difference between bread flour and all-purpose flour was significant. There's no one flour that's right for every purpose, and of course I didn't test every option. The point is that different flours will behave differently, so even if you weigh every ingredient, your results may not be consistent unless you're using the same flour—and if the flour itself is consistent from the manufacturers.