This is a great topic, ripped "straight from the headlines" (aka Google searches). And it has a lot to do with the actual definition of what puppets are:

Most definitions consider a puppet to be an inanimate object, which is then manipulated (or ‘animated’, or if you prefer, given life) in order to produce some sort of movement. We can extend that definition to state that the object is anthropomorphised (given human personality, or in the case of animals, given animal characteristics). See the post on ‘what is a puppet show‘ for more discussion on how puppets are used.

So how does this relate to silhouettes? Well, it’s a slight but important difference.

A silhouette, which was popular in the Victorian era, was simply a cut-out piece of paper or card, in the shape of something; usually a person’s bust (head, neck and shoulders). Silhouettes were often done on profile, showing half of the person’s face. It’s sort of like doing portraiture in shadow. These silhouettes were usually then mounted and displayed, much like paintings. 

A shadow puppet, while technically being a silhouette (and the only puppet type which you actually watch the shadow of the object, rather than the object itself), is not the same thing. A shadow puppet can yes, be a cut-out piece of paper or card, and yes, be the shape of a person’s head. However the difference is that in this case, the silhouette is being manipulated in order to produce a movement or effect. Additionally, barring some French and Asian shadow puppets, historically the shadow puppet has a number of sections to it, which are jointed together, allowing more movement and action.

So in the end, we can say that:

• A silhouette is a decoration or item for display
• A shadow puppet is an object designed for interaction and movement

How to make a shadow puppet screen is discussed here; free patterns are here; making shadow puppet joints can be found here; materials discussed here; how to make a shadow puppet is here AND here. Shadow puppets and patterns available here.