My job as a grappler is to stop your movement standing up so I can put you on the ground. Then I transition into static stability. When I mount you, it is static stability with constant adjustments to keep the mount. When I am standing, if I keep moving, it is easier for me to avoid you punching me in the face. But whether on the ground or standing, balance is the key.
Stability is a fluid thing in a fight.
But balance is the key. IF you keep your balance, you will do well in the fight. Maybe not win, but do well. I think that we are closer in ideas than words can say. I am looking at the leg of the elephant and you are looking at it's ears.