Stability is the ability of a component or structure to remain stationary or in a steady state.
An airplane flying forward could be said to be stable, but a ball sitting on a table is unstable. The plane, on the other hand, resists movement because of the flight control surfaces. Determinacy is the ability to compute support reactions using plan statics. That is, if a structure is determinate, the equations of equilibrium are sufficient to find all the forces. If it is indeterminate, there are too many reactions to solve for.