Here is the final definitive explanation of the "posi" thing. It is a tradmarked name, but not by the car manufacturer, but by the manufacturer of the differential unit, Eaton.
Positraction, or Limited Slip
Limited slip rearends work in exactly the same way, but, they resist this "turning at independant speeds" idea, by installing a set of clutches (or something else that may act like a clutch) on one, or both axles, and "hooking" the axle, or axles, to the ringgear carrier. The clutches are set to slip at a certain torque. By design, as input torque, from your engine, increases, the clutches hold on tighter, in an attempt to keep both axles turning at the same speed, relative to each other. When one wheel has no traction, a limited amount of torque is applied to the opposite axle, hopefully helping enough to get you "unstuck". And the difference between "Posi", "Limited Slip", "Traction LOK", etc? They have all become generic overused terms that basically can be used interchangeably. "Positraction" is a Trademark name, just as "Traction LOK", but have become generic terms, just as "Cresent Wrench", and "Channellocks", although both being specific brands, have become generic terms. ("CresentWrench" is a particular brand of adjustable wrench, and "Channellock" is a particular brand of adjustable slipjoint pliers). Another example is the term "COKE", which many people use as a generic term meaning Cola, even though "COKE" is a particular brand of Cola.