The darkness in the shade does not work the same way as dark-colored things that are put directly in the sun. It is true that darker colors in the sun absorb a lot of sunlight and becomes very hot, but for the shades that trees and buildings give us, it is not that the shade is a "color" like the darker colors. The shade is actually the absence of a lot of sunlight, because whatever is providing the shade is absorbing the sunlight already and stopping the sunlight from reaching the shaded places. Furthermore, shades look darker because of the absence of sunlight, whereas darker-colored things look darker because of the dyes in these things (for example, a black jacket).

In other words, shades will not look dark or like shades at all if we take away the thing that's giving us the shade, but things that are darker-colored will look that color whether we put them in the sunlight or under lamplight. Knowing all this, we can see that places with shade - places with little sunlight - would of course keep us cool, while darker-colored clothes actually absorb sunlight and make us warm/hot.