There is a difference, but it gets kind of wordy. A thing (tree, building, person) casts a shadow but gives shade. We sit (and cows lie) in the shade of a tree. The tall building made the entire street shady. But a potential attacker lurks in the shadows.

Being "in another person's shadow" could literally mean you're standing in the dark shape they cast on the ground, but most of the time it's taken to mean that, no matter how wonderful your deeds have been, the other person's deeds have been greater, received more recognition, etc.

Then there is the not-much-used-but-still-commonly-understood use of the word shade to mean a ghost. The Widow Wonka thought she saw her husband's shade looking in the window.

Was that clear enough, or not yet?