Shade is the general dark area that is protected from the sun:
It's so hot out - let's sit in the shade.
We brought an umbrella to the beach so that we could have some shade.
A shadow is the "shape" of an object or person that blocks the light. You can only have "shade" from the sun, but you can have a "shadow" from the sun OR other types of light, such as electric lights or candlelight.
My dog is afraid of his own shadow.
A lunar eclipse occurs when the moon passes through the earth's shadow.
We can also use the word shadows to refer to a dark area in general:
He jumped out from the shadows of the basement and scared me half to death.
If you stand behind a tree trunk or a round pillar on a windy day, you will notice that if offers no protection, and a lighted match will be extinguished. A small experiment at home will confirm this blow hard against a bottle which has a burning candle standing behind it, and the flame goes out at once. The air current divides on hitting the bottle, clings to the sides, and joins up again behind the bottle with its strength hardly reduced. It forms an eddy which hits the flame. You can put out a lighted candle placed behind two bottles in this way, if you have a good blow.