An instance of an image is called a container. You have an image, which is a set of layers as you describe. If you start this image, you have a running container of this image. You can have many running containers of the same image.
You can see all your images with
docker images whereas you can see your running containers with
docker ps (and you can see all containers with
docker ps -a).
So a running instance of an image is a container.