In the vids you posted originally, one is on stones while the other one is on leather. Pretty much forces edge trailing in the second case.
On stones well to get your burr you need edge trailing. So it doesn't really matter how you do them, scrubbing figure eight pure trailing, but it's when you trail that you really form the burr and fully "project" it on the other side.
Problems some encounter with scrubbing is they apply as much pressure leading then trailing in the motion, which tends to "hide" the burr since you're basically removing parts of it as you form it. Eventually it works up but you may be removing more steel than needed.
For deburring, I think the catch is this:
trailing = less chances to mess your apex, more chance to not deburr properly
leading = more chances to mess your apex, less chances to not deburr properly
I sort of apply the "wrong" scrubbing idea in deburring because that's exactly what I want: I'll start with trailing some, convert to trail-lead in a same stroke and equivalent pressure halfway, and finish with only leading strokes. That where I really decrease pressure until close to none.
Last fine stone of a progression I might ultimately add a trailing strop motion but 1-2 strokes per side only and no pressure. Or not. There are visual clues and tactile clues in deburring that are relatively easy to learn to recognize. Also steel and what grits you're on helps to determine how to best get there.
There are I guess very different techniques and schools of thought about this, and someone who controls them well will achieve the goal. But whatever the differences a sharp clean edge is one thing only. How you get there is debatable, but getting it is not. You just need to find what works for you with your knives and stones.
