A shadow is the shape that something makes when it blocks out light. It's a common word, and you see shadows all the time.
A silhouette is a relatively uncommon word, and means the sideways shape of something. It is usually only used for 'complicated' shapes. It could be a shadow, but it could be (say) a piece of paper that is cut out to the same shape that a shadow would be.
It could also refer to when you can't see some object, but you can see a bright background behind the thing. The object appears as a dark silhouette in front of the light background. If the object is not illuminated, it will not have a shadow at all.
For example - you would normally only refer to a side view of a person as a silhouette - i.e. if you could see the shape of the nose and eyebrows. You would not usually refer to a front view as a silhouette.
Some shadows would be silhouettes, but most aren't. You would not call an indistinct shadow or the shadow of a simple shape such as a plain rectangular building a silhouette.