shadow noun 1. a dark shape cast on a surface when an object stands between the surface and the source of light.
shade noun 1. the blocking or partial blocking out of sunlight, or the relative darkness caused by this.
[Emphasis in definitions added.]
A shadow has the specific shape of the item that is blocking the sunlight. If you are walking along the road in the sun, you will see your shadow on the pavement (side walk) - it has the shape of your body and moves along with you. You cannot stand in your own shadow because your body is creating the shadow.
Shade is a more general (and usually larger) area blocked from direct sunlight by buildings, trees, etc.. You may be able to distinguish individual shadows or partial shadows within the shade, but often cannot do so because the individual shadows of trees, buildings, etc. have all merged into a larger area of shade.
P.S. I am answering from a British English perspective. As far as I know, the words are used the same way in the USA.
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