Resilience determines the persistence of relationships within a system and is a measure of the ability of these systems to absorb changes of state variables driving variables and parameters and still persist. In this definition resilience is the property of the system and persistence or probability of extinction is the result. Stability, on the other hand, is the ability of a system to return to an equilibrium state after a temporary disturbance. The more rapidly it returns and with the least fluctuation, the more stable it is. In this definition stability is the property of the system and the degree of fluctuation around specific states the result.
Holling, C.S. (1973). Resilience and stability of ecological systems. Ann. Rev. Ecol. Syst. 4, 1-23: 17.