Stability refers to the ability to remain in a certain state. The "state" in some instances can be dynamic, and in other instances it can't.
Stability in chemistry refers to elements or compounds that not reactive (don't "want" to continue combining with other elements to acheive stability). The Noble gases Ne, He, Ar, etc. are very stable. While some elements and compounds are
stable at STP (standard temperature and pressure) others are not, yet they may be stable at high pressure and low temperature for example. Everything might be deemed "stable" at absolute zero in a chemical sense. The equilibrium state of a controlled chemical reaction would be stable even though chances would still occur at a certain rate.
Stability in a physical sense is an object's ability to remain in a certain position without movement.
There is financial stability, emotional stability, economic stability, environmental stability, genetic stability...all are dynamic systems that change within a certain set of parameters (so unstable in the strictest sense) but are stable in a broad, overall sense as long as they remain/perform within certain guidelines.