In Docker, it all begins with an image. An image is every file that makes up just enough of the operating system to do what you need to do. Traditionally you'd install a whole operating system with everything for each application you do. With Docker you pair it way down so that you have a little container with just enough of the operating system to do what you need to do, and you can have lots and lots of these efficiently on a computer.
Use docker images to see the installed images and docker ps to see the running images.
When you type docker run it takes the image, and makes it a living container with a running process. I tend to use:
docker run -ti : bash
Lastly, images have their own set of ids and containers have their own set of ids - they don't overlap.