Not the other way around.
The driver is usually the relationship that drives the story. Eg. one person is trying to remember something and the other one is trying to help them remember. It should be simple, should not change, should lead to a change in the situation. (Ok, so trying to remember something is probably only a scene in a story, but nonetheless it is works the same. A scene is a story too. But if it was amnesia it could be the whole story.)
What makes the story complicated, interesting and satisfying, is what you manage to do with the driver. The story becomes complicated with time passing. The person trying to remember might jump around, talk about all sorts of other things. The person trying to make the person remember might get irritated, cross, they might laugh, employ strategies etc etc etc. Anything that can spin off that simple "driver" is the story. When the person remembers what he had forgotten, the story is over.
What often happens is people make complicated drivers and simple stories. Complicated drivers confuse audiences, and simple stories bore them. Bad combo.