Okay, just to clarify something:
Both controllers still run wireless signals when you connect them to their systems. However, the 360 controller won't store sync data if you do not leave a battery in the controller when connecting it to the system, in essence gaining the functionality of a wired controller but still sending a wireless signal to the system.
The PS3 is just like it but since you can't remove the battery, it's always going to be synced to whichever PS3 it is connected to physically even if the charging cable is severed.
Both controllers still run wireless signals when you connect them to their systems. However, the 360 controller won't store sync data if you do not leave a battery in the controller when connecting it to the system, in essence gaining the functionality of a wired controller but still sending a wireless signal to the system.
The PS3 is just like it but since you can't remove the battery, it's always going to be synced to whichever PS3 it is connected to physically even if the charging cable is severed.