Unfortunately, the way an automatic transmission uses overdrive is not quite as simply as a manual transmission, simply based on the fact that automatic transmissions are more complicated pieces themselves! An automatic transmission uses a torque converter to transmit power via the engine and transmission, whereas a manual transmission Mustang uses a direct clutch. Without diving too deep into the workings of a torque converter, a basic overview is probably needed.
A torque converter is used to transmit power from the engine to the transmission, as mentioned above. However, the fashion it does so is completely different than a typical clutch setup. Torque converters rely on fluid couplings between two halves to transmit power. The impeller half is connected to the engine, whereas the turbine half is connected to the turbine shaft (which connects to the transmission). As the engine revs up, the impeller side spins (remember, impeller side is directly connected to engine), pushing transmission fluid (a special oil) over to the turbine side. Due to some very cool physics and engineering (which we will not discuss here), the turbine side rotates, which rotates the turbine shaft and subsequently turns the transmission.
With that said, the good news is, it gets simpler from here. The important parts are: 1) impeller is connected to engine, and spins at same speed; 2) impeller pushes fluid to turbine side, which rotates turbine at a different speed. Wait a minute, this looks like the classic formula… input is greater than output, therefore the converter is slipping. When overdrive engages in an automatic transmission, it rectifies this converter slip by locking the converter (i.e: converter turns at engine speed) and then engages special planetary overdrive gears within the transmission.
Having written all that, I suppose that overdrive within an automatic transmission does not work very differently than a manual transmission. The concept is the same – use a special gear that when driven, has greater revolutions than is applied. The complicating factor for automatic transmissions is the torque converter (the ‘middleman’).