Latent and sensible heat.
Two kinds of work an AC does. The thermostat only measures one of them.
An air conditioner does two different jobs at once, and the names for them explain a lot about why a house can feel wrong at the right temperature.
Sensible heat is the heat you can feel with a thermometer. Removing it lowers the air temperature. That is the part a thermostat measures.
Latent heat is the energy held in water vapour. Removing it condenses moisture out of the air on the evaporator coil and sends it down the drain. It lowers humidity without lowering the temperature reading at all.
Every system splits its total capacity between the two, and the split shifts with conditions.
Why Phoenix is two climates
In June, with a dew point in the thirties, there is almost no moisture to remove. Nearly all of the system’s capacity goes into sensible cooling, which is why dry heat and a working AC feel so effective.
In August, with monsoon moisture in, a meaningful share of the same capacity goes into latent work instead. The system is doing more total work and the thermostat sees less of it, because much of its effort is going into water rather than temperature.
That is the honest answer to why the house feels different in August at the same setting, and the monsoon humidity guide covers what to do about it.
Why run time matters so much
Latent removal only happens while the system is actually running and the coil is wet. A system that satisfies quickly and shuts off removes temperature and barely touches moisture.
That is exactly what an oversized system does, and it is why oversizing produces a house that is cold and clammy rather than comfortable.
It is also why running the fan on ON rather than AUTO makes a house damper: water sitting on the coil after the compressor stops gets evaporated straight back into the airstream.
What it means for diagnosis
Delta T alone cannot tell you how a system is splitting its work. Dry bulb and wet bulb readings together can, and that is part of why a proper check-up measures more than one number.