FLEXIBILITY is the PASSIVE range of motion (PROM) that exists in your body. It’s dictated by the extensilbilty of your fascia, muscles, joint capsules & nerves.
MOBILITY is the ACTIVE range of motion (AROM) that you possess. Basically its the control you have over your PROM.
There’s always a difference between your PROM & AROM. If you want to move & function well, then you need that difference to be as small as possible.
To do this, work on your FLEXIBILITY by STRETCHING, then on your control of that FLEXIBILITY with MOBILITY exercises.
Without good FLEXIBILITY then your joints can’t move into a normal ROM & without good MOBILITY then you can’t control your joints. So you need them both!