Desktop Computers are personal computers that can only be used in a single location on a desk or a table hence the name 'Desktop' Computers. Desktop Computers have no internal source of power so they need to be always plugged-in in order to operate.
The advantage of Desktop Computers is that they can be upgraded. You can increase the RAM, the Internal Storage and Graphics. You cannot increase the Motherboard capabilities but you can replace it if you want for a more powerful Motherboard.
A typical desktop comes with the Monitor and body separated. However, in an All-in-One Desktop, the computer components are all integrated into the Monitor. Instead of getting two parts, you get a single Monitor that houses all computer components.
The Advantage of All-in-One Desktop is that it is compact taking less space. The Disadvantage of All-in-One Desktop is it's hard to upgrade its components.