Stability is often shorthand that specifically refers to short-term transient stability of a system after a fault. Typically transient stability analysis ignores phenomenon faster than 0.25 cycles and slower than 30 seconds. Usually a power system transient stability study looks at just one outage at a time. In the USA, the specific outage types are described in NERC standard TPL-001.
Resilience often covers a broader time range. Several minor individual faults throughout the day end up pushing the system outside of prestudied stability boundaries into unknown operating conditions as dispatchers reconfigure the system. Resilience may also include addressing many other kinds of stresses including storms, earthquakes, wildfire, drought, fuel disruptions, transportation disruptions.
Stability could also refer to voltage stability, small signal stability, or frequency recovery capability.
This forum has folks from all over the world, and it is always interesting to hear when other regions use terms differently than where I live.