Oh I see how that can be confusing. They are very different things.
To explaing it requires a litle undernation of how the collision works.
The collision system is based on a especial case of a theorem called the Minkowski difference of two polyhedral.
https://en.wikipedia.org/wiki/Minkowski_additionthe special case is that the Mink Diff of tow convex polyhedral is another convex polyhedral and this is true in all dimensions. so to explain we use a two d system.
basically to build a naïve the mink different of two polygon you build an array of vector in which for point of polygon A you subtract all vertices of polygon of B.
This generate a vector of point and the convex hull of that new set of point is the Mink difference.
this is very expensive to do taht way, so the are tow algorithm thet came to tyeh resques.
1-The GJK algorithm
2-Quick Hull algorithm,
GJK is much faster but it only functional when the two shape do not overlap each oether.
and here is where it becomes difficult because for collision because a collision system
are interested in intersection of shapes.
Most collision systems are variance of those two algorithm in some for ot another.
So what most people do is the they assume the shapes do not overlap and run GJK, and three things can happens.
a) the shapes do not overlap which is determine if the origin of the Mink diff is outside the shape.
b) the shapes overlap which is determined if the origin of the Mink diff is inside the shape.
c) the shape touch on the surface determined if the origin of the Mink diff is on the surface.
case a and b and clear cut, case c is very hard to resolve because as the shapes get closer and closer
the distance from the origin to the surface become smaller and smaller and numerical errors start to creep in to the point where you can get a collision point that is numerically correct and geometrical incorrect. Unfortunately case C is the most common one for a physic engine.
To go around that problem, most system do not allow for case C to ever happen and as soon and the distance to the surface point falls below some small value, they declare an acceptable collision and use that as collision point. That small distance is what in newton is called the Material Skin thickness. Therefore Material Thickness is the is the distance between two shapes and does not affect the shape themselves.
When the distance happen to be smaller, the algorithm declare penetation and resolve collision
using the quick hull algorithm.
some people like to pretened they invented something, and renamed it expanding polytope because the algorith does a directed guided search to the point close to the surface. but this is just a quick hull with another name.
Quick Hull can be used to resolve collision in all cases because is general and it never ever fail,
however is far more expensive that GHK, and that's what justify using two algorithm instead of just one.
Early versions of newton did not used GJK, instead used Quick Hull for every thing, but after 2.xx I start adding GLK reluctantly, and say reluctantly because GJK is one of those algorithm that are numerically unstable, very prone to give you wrong answer that are numerically valid.
This is why in newton, I still use Material Skin thickness set to zero to force all collision to report penetration and resolve using Quick Hull, GJK only used mostly for sophisticated trivial rejection test. Basically for calculating distance between two pair and decide if they need to calculation contact or not.
The new Parameter works on the shape by making it smaller, but I explained that already.
I hope this is clear.