As used in the US for "dry stuff," the "cup" is a measure of volume. A working definition is that it's the volume occupied by a half-pound of water.
Since the density of things varies widely, a "cup" of flour will be a much smaller weight than a cup of water - and a cup of "sifted flour" will be a smaller weight than a cup of "unsifted flour." A cup of whole-wheat will be a different weight than a cup of "refined" flour.
While the common Euro practice of weighing things is significantly more "precise" than the US practice of measuring by volumes, most recipes are so inaccurate that precise measurement is somewhat over-rated.
Since a recipe always calls for a "cup of something" a "density" is implied, and the conversion is built in - if you measure by volume. Most practiced cooks use handfulls, splashes, glugs, glurks, pinches, dashes, and sprinkles in their actual cooking
(3 glurks is the amount you get when you tip up a small bottle until it goes "glurk - glurk - glurk." A glug is the corresponding measure for a large jug.)
A few recipe books - mainly those for special diets - give conversions between volume and weight, but the conversion depends on the specific thing being measured.