Running the fan of a single home residential air conditioning unit does consume electricity, but compared to running the compressor (which cools the air), it generally uses significantly less power. The fan's primary function is to circulate the cooled air throughout the home, and its power consumption is relatively lower than the power needed to actually cool the air.
When the thermostat is set to "auto," the fan will only run when the air conditioner is actively cooling the air. Once the desired temperature is reached, both the compressor and fan will turn off until the temperature rises again and the cooling cycle needs to restart. This can result in more efficient energy usage since the fan is not running continuously.
On the other hand, setting the thermostat to "on" will keep the fan running continuously, even when the compressor is not actively cooling the air. While this can help with better air circulation and filtration, it also means that the fan is using electricity constantly, which can lead to higher energy consumption and potentially higher utility bills.
In summary, if energy efficiency is a concern, it is generally better to set the thermostat to "auto" so that the fan only runs when the air conditioning unit is actively cooling the air. However, if you prefer a more constant airflow and improved air circulation, setting the thermostat to "on" might be more suitable for your comfort preferences, but it will result in a slightly higher electricity consumption.