Just cleansed a point and enabled edge climb … exactly the same.
…and here’s the tooltip…
“Unlocks the ability to climb up any nearby edge after performing a jump or using the grapple.”
My original statement stands!
Personally… if I could already climb up from grappling, I would never activate the edge climb skill.
Edit: tested again, edge climb automatically makes you jump up when near the edge (even when grappling). Still seems like a semi-pointless skill to have if you can already manually jump from the grapple anyway.