The xbox Cable controller is a controller that requires the use of a cable. The xbox Wireless controller is a controller that allows you to play without a cable. The wireless controller needs to be charged or it won't start. The wired controller does not need to be charged, as long as it is connected to the xbox console, you can have fun. However, for small partners, in the current era of everything wireless, or wireless handle is good.
Wired needs to be under the connection line to use, wireless can be used in Bluetooth mode