Or the almighty 2L73, yeah baby, highway gears! (ugh)
Posi is the GM term for it. They had it first, now its kind of like Kleenex. I think they even Copyrighted that name. Track-lok and Posi are both names for limited slip.
If one tire is lighter in a corner, would be a weight thing. Once you get them both spinning, they will leave the same mark in a straight line. Around a corner the inside tire will leave a lighter mark because there is less weight. You can see this effect exaggerated with a Mini Cooper, which will pick the entire inside rear wheel off the ground.
If you think you Limited Slip is shot, a straight line test is the only real way to be sure, without a "real" test of the part.