Let’s start with the basics–
A cookie stencil is a thin sheet of polyester film, plastic, or acetate with a pattern or letters cut out of it, used to produce the cut design on the surface below by the application of icing or airbrush colors through the holes. I took this from the dictionary, but changed it to cookie language. I always buy food safe plastic. If I am unsure, I call the manufacturer.
Here are what I call the parts of a cookie stencil. I am sure there are more technical terms, but I want to keep it simple.