I am new to Corvette and its history but have been learning about them recently and know that the C5 and C6 both came factory standard with LSD (Limited Slip Differential: "Positraction": a GM-coined term). Corvette has utilized LSDs for decades as the technology is not new and dates back at least to the 1960s (Ferrari has used it for at least that long).
The differences are:
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LSD: There is a clutch mechanism within normal LSDs that engages when the first wheel starts to slip. This is old-skool derived and called "Positraction" in the muscle car world. The C6 and most all other Corvettes use a friction based clutch pack. They are spring loaded on the C3, C4, C5, and C6, and apparently on the base C7.
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VLSD: Viscous Limited Slip differential (common in European and Japanese sports cars such as Ferrari and Nissan, et al): Uses a sealed unit that contains a silicone-based fluid that heats up when the first wheel starts to slip and then engages the other wheel. It typically grabs faster than the LSD-clutch type.
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eLSD or "E-Diff": Corvette C7 Z51 option: A smart electronic limited-slip differential (eLSD) that continuously makes the most of the torque split between the rear wheels. The system features a hydraulically actuated clutch that can infinitely vary clutch engagement and can respond from open to full engagement in tenths of a second. It shifts torque based on a unique algorithm which factors in vehicle speed, steering input and throttle position to improve steering feel, handling balance and traction.
The eLSD is fully integrated with StabiliTrak and Performance Traction Management systems. Its calibrations vary among three modes, based on the Drive Mode Selector setting:
• Mode 1 is the default setting for normal driving and emphasizes vehicle stability
• Mode 2 is engaged when electronic stability control is turned off in the Sport or Track Driver Modes. This calibration enables more nimble turn-in and traction while accelerating out of a corner
• Mode 3 is automatically selected when Performance Traction Management is engaged. This calibration has the same function as Mode 2, but is fine-tuned to work with Performance Traction Management.
I hope this synopsis answers some lingering questions from fellow C7 enthusiasts
