Recoil pressure is the difference in pressure between two sides of an elastic structure. To get any hollow elastic structure to move from its resting volume, one side of the structure must be exposed to a higher pressure than the other. In respiratory physiology, recoil pressure is used with respect to the lung and the chest wall. It is always the pressure inside minus the pressure outside.
The recoil pressure of the lung is the alveolar pressure minus thepleural pressure (inside pressure minus outside pressure). Other terms which refer to the exact same quantity are the distending pressure of the lung, the transpulmonary pressure, PL, and Palv - Ppl. While Palv and Ppl can be positive or negative, the recoil pressure of the lung is always be positive; that is, the alveolar pressure must always be greater than the pleural pressure. The greater the difference, the greater the recoil pressure, and the bigger the lung will be.
The recoil pressure of the chest wall, which can be measured only when the muscles that make up the chest wall are relaxed, is the same as the distending pressure of the chest wall, which is the same as PW, which is the same as Ppl - Pbs. All refer to the difference between the pleural pressure and the pressure at the body surface, which is atmospheric, and therefore zero.
The recoil of the respiratory system, or PRS, is simply the recoil pressure of the lung plus the recoil pressure of the chest wall, which is Palv-Pbs.