If you have say 50k miles and have hammered her like shes built for and change your diff oil and its black, the black is the clutch materials, large odds are cracked belleville springs too.
I was told not to waste cash on a new diff only to smoke the frictions and crack the springs. I purchased one with 65k miles and found what you see in the pics.
The OE has only three frictions, the Z06 and HHP kits have 7 surfaces.
Some people read what Friction Modifier is. I gets in the frictions making them more forgiving in the u-turns. Too much and you take away performance. If its intolerable add one ounce at a time.
Lots of these diffs get ruined at the track in the water box if one side gets wetter and the other gets traction before the other it will smoke the other side. The Z06 kits solve this. Irt will be more aggressive in the turns and most use oils with the FM already in it and are happy.