AC power cord different on a laptop and a desktop, other appliances
Yes. IEC 60320 covers these connectors. The Mickey Mouse connector is C5/C6 (Female/Male). The boxier connector is C13/C14. The reason for one over the other is mainly size and Amperage (and therefor temperature). C5 is rated for 2.5 Amps Main Voltage. C13 is rated for 10 Amps Main Voltage. Any power supply over 300W will not be able to use the C5. Most laptops are under 100W.

Additionally the ATX computer form standard calls for the C13 connector. Even smaller than 300W power supplies in ATX format uses them.