The main difference between a wired bike sensor and a wireless bike sensor is a wired sensor uses the computer as a power source via connection by wires to the computer battery (i.e., a wired bike computer only has one battery located in the computer). If the sensor has stopped working but the computer still works, chances are there is a break in one of the wires that runs from the sensor to the computer.
A wireless sensor has a separate battery in the sensor that powers the sensor to send the wireless signal to the computer/receiver.