My understanding is as below. Please correct me if wrong.
With A/C on and with auto selected, the car decides the airflow direction and fan speed, whilst maintaining the temperature at the selected setting. If the temperature of outside air is colder than the internal temperature, engine heat is used to warm the interior to the desired temperature and if the outside is warmer than the internal temperature, the A/C unit chills the outside air to the desired temperature.
It A/C is switched off in auto mode, the same applies but the A/C isn’t used, so if the internal temperature is more than the external temperature, the car can only allow the external air to be drawn into the car unheated, at whatever temperature it may be.
Eco mode allows the tolerances of the selected temperature to be exceeded, reducing the energy required to maintain an exact temperature level and recirculation recirculates the internal air, reducing the need to heat/chill ‘fresh’ air from outside the vehicle. Unsure if any external air is mixed with the internal air in recirculating mode or whether external air is completely blocked, with only internal air being recirculated. In auto mode during hot weather, the recirculation function can switch on automatically for extended periods, to aid cooking through the reuse of already chilled internal air. Switching off auto mode allows manual control of fan and air flow direction. Off switches the system off, so no fan running. Unsure if any air is allowed to enter the car without fan boosting within off mode, with air being directly at the last used auto/manual direction.