Cabinetman, those are flexible, self adjusting mounting tabs that are used when the slides are directly attached to the cabinet sides. They have nothing to do with a soft close function. Most slide installations only attach at the front and rear, typically using a rear bracket. DIYers often attach to cabinet sides but that is rare in the industry.
Most of the better quality manufactured cabinets use soft close, self closing slides these days. There is either a spring or hydraulic piston mechanism that engages with the slides. They prevent the drawers from slamming back into the cabinet which can shift the contents. These mechanisms act to complete the drawer closing. You just push the drawer partially closed and the mechanisms take over softly closing the drawer. With some, there is an interruption, so to speak, as you pull the drawer open and disengage the mechanism. Less expensive slides often work less smoothly when opening the drawer than the better slides. Blum Blu-motion slides are the industry leader and most cabinet manufacturers will advertise that these are what they use. Educated kitchen customers often ask for Blu-motion. Undermounts are particularly popular sine the slides are not visible when the drawers are opened, showing the dovetailed drawer sides. This is mostly for dedicated followers of fashion but a lot of folks have jumped on that band wagon. You got to keep up, Bro!