The difference is between dry and wet adiabatic lapse rates. The dry adiabatic lapse rate is the rate at which dry air cools as it rises (or warms as it descends): a loss of 5.4 degrees per thousand ...
When dry air (meaning no clouds) changes pressure, it also changes temperature. If you have ever filled a bicycle tire, you may have noticed the more air you pump into the tire the warmer the valve ...