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.
This Colorado hotel holds regular ghost tours during the month of October, telling the stories of unexplained paranormal activity reported by former guests and staff through the years. The tales have included sightings of a railroad conductor as well as a string quartet in the San Marco Room, where musical performances were held. The quartet reportedly asssured the bellman who spotted them saying We live here.