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.

A silhouette is a darkened shape or outline of something. A shadow is the darkened shape that occurs because of a light source being blocked.

In both a silhouette and a shadow, a light source is being blocked. In a silhouette, the light, the eye and the shape are in a line, and the eye sees the darkened shape. A shadow is cast when the light is blocked and it creates a visible image on something else. You see a silhouette when you are looking at an object from its shadow.

Cole is right. If you look at someone with the sun behind them - you see their silhouette A person standing in the sun casts a shadow - the shadow is the dark shape of that person on the ground