Why do laptops need a higher voltage than desktops? Also, what form factor do laptops use?

Laptops typically do not have power supply units (PSU), like desktops. Since laptops are designed to be as light and thin as possible, putting a PSU in the laptop is not feasible. There are some electrical regulation components in the laptop, to make sure the power coming in the correct voltage and amperage. However, laptops PSUs are the "brick" in the power cable. That is what converts the alternating current (AC) from the wall's power socket to to direct current (DC), which the laptop uses. Laptops do not conform to form factors, like desktops. There is no AT, ATX, mini, micro, etc. Again, since laptops are designed to be as light and thin as possible, the design of every laptop is unique.