Joint stability is the ability to control the position of the joint during movement.
Joint stability relies on muscles located closer to the joint.
These smaller muscles are usually located deeper in the body and are different from the large muscles that lie near the surface. That is our segue to joint mobility.
Flexibility is passive.
Flexibility is the ability to move through the range of motion without muscular control, and without necessarily keeping the joints stable.
Mobility, on the other hand, is active.
It is the ability to use muscular control to move in and out of the pose (or chair, or vehicle) while keeping the joint stable.
Mobility is a concerted effort of all muscles around the joint - those that lie deep near to the joint itself, and those that lie further away, closer to the surface of the body.
In daily life, an example of mobility would be the ability to get down to the floor and get up off the floor easily.
Without this all-together-now effort, muscles and joints get uneven use.
Some get used way more than what they are built for.
Some get used way less.
Some don't get used at all.
Strength is the function of mobility: if we can't control the range of motion, we are much more likely (as you now know) to experience discomfort or injury.
Whether you are concerned with reducing pain or building strength (and hopefully both!), the path to getting better is one and the same:
recover stability,
re-establish mobility,
get stronger!