DO shadow and shade mean the same?
A similar meaning, but not the same. We use them in different ways.
'Shade' is basically the opposite of sunlight. It refers to an general area which is protected from sunlight in some way.
If you don't want to be in the sunlight, you can sit in the shade. You can sit under the shade of a tree or a parasol. In very hot countries, it is recommended that you should stay in the 'shade' around midday. You wouldn't use 'shadow' here.
'Shadow' is more specific. A shadow is the dark shape projected on to a surface by a particular object. A shadow is a similar shape to the object which casts it. The shadow of a person is different from the shadow of animal, for example.
For example, you might say. 'She saw the shadow of a man move across the window'. This is a shape. You couldn't use 'shade' here.