I don't know why you are so confused about S Speed / the small gap. This speed is only important when you are NOT in Conf 1 and therefore slats are not deployed.
S speed is the lowest speed to select flaps 0 (during climb). While descending it's the "opposite": When you are not in Config 1 (in other words clean) you have to set Flaps 1 at least at S Speed. With Flaps 1 you can come below S speed without any problems.
Similar with F Speed
F Speed is Minimum Flap Retraction Speed while climbing. That means on Approach that you must have Config 2 (flaps deployed) at F Speed.
If you go to the next Flap Lever Position at VFE next, F und S are only a kind of last warning speeds.
So far my understanding.
Regards