A printer is a device that lets you produce a copy of a document, or a picture such as a photo, onto paper. You may take this with you, or display it.
This is a set of instructions that your computer understands, and that you tell the computer to run. It will often be displayed in a menu, or perhaps represented as an icon on your screen. Typically, you don’t get to see the instructions, but they’ll be there, just the same.
A router is a device that directs your internal network’s traffic between the different components within that network.