Rupture deals damage to your target when you are not in melee range of it. S&D does not cause you to do damage to your target when you are not in melee range of it.
Rupture deals bleed damage which is not reduced by armor. White attacks buffed by S&D are physical damage and are reduced by armor.
The entire duration of Rupture can only be applied to one target. During S&D you can freely switch targets and damage different ones.
They don't resemble one another in any meaningful way.