Given that the dry and moist adiabatic lapse rates are different, it is possible for a parcel in equilibrium to act differently after being disturbed, depending on whether it is unsaturated or saturated. Remember, the dry adiabatic lapse rate applies for an unsaturated parcel, the moist adibatic lapse rate for the saturated parcel.

If the environmental lapse rate is less than the moist adiabatic lapse rate (and by default, less than the dry rate), the parcel is in stable equilibrium regardless of whether it is saturated or unsaturated (recall the criterion that environmental lapse rate < adiabatic lapse rate for stable conditions). So, the atmosphere is absolutely stable---it is stable for any parcel condition.

If the environmental laspe rate is greater than the dry adiabatic lapse rate (and by default, greater than the moist rate), the parcel in unstable equilibrium regardless of whether is is saturated or unsaturated (recall that environmental lapse rate > adiabatic lapse rate for unstable conditions). So, the atmosphere is absolutely unstable---it is unstable for any parcel condition.

When the environmental lapse rate is between both adiabatic lapse rates, then we have an interesting condition. Since the environmental lapse rate is greater than the moist adiabatic lapse rate, a saturated parcel would be in unstable equilibrium. However, if the parcel is unsaturated, we use the fact that the environmental lapse rate is less than the dry adiabatic lapse rate, which suggests that the parcel is in stable equilibrium. The atmosphere is described as conditionally unstable---it is stable or unstable depending on whether the air is unsaturated or saturated, respectively.