Choose the friction you actually want to remove
Repeated clicking is the problem
Auto Roll is the closer fit. Its observed controls automate the next roll and let the run react to selected rarity targets.
Waiting is the problem
Fast Roll is the closer fit. It visibly shortens the sequence, but no reliable source supplies an exact speed multiplier.
Neither checked effect proves better luck. If you do not roll often enough for either friction to matter, the evidence supports buying neither.