Understanding the difference between common standard printers and a 3D printer is best with knowing what each of them were, before comparing them.
A common standard printer use papers, and have the capabilities of four different things: printing, faxing, scanning and copying. These four functions are performed with a papers. Most printers have the ability to print on both sides, but it requires some additional steps, like turning the papers after they have been printed on. There are some printers that would print on both pages without any additional steps, than the setting, and there is no need for any turning of papers. But it only prints, scan, copy and fax on a plain two-page paper.
A 3D printer on the other hands would create an object out of hundreds of materials, directly from a digital file. These objects can be from a simple object to a much more complex object like a human organ. It uses hundreds or thousands of layers to perform its duties. It is highly capable of being more productive in presentations that include prototypes, or parts of an airplane engine.
The difference can be simply put in summary, a common printer will print anything, but on a plain paper, while a 3D Printing will create object with any material that is beneficial to the project.