What types of S-Functions are there and how are they connected to each other?

I would like to understand the connection between different types of S-Functions. I'll try to draw my own picture and would appreciate if you someone could confirm it.

S-Funcitons

 MATLAB S-Functions

   Level-1 MATLAB S-function
   Level-2 MATLAB S-function

 C MEX S-Function

   noninlined S-Funcitons
   wrapper S-Funcitons
   fully inlined S-Funcitons

That would mean there are in fact five different types: Two of them are MATLAB S-Functions and Three of them are C MEX S-Functions.

I'm really totally puzzled because on the MathWorks Help-Page I am send from one topic to another without having any overview what exists.

At last I want to know: If I create a wrapper S-Function and include it in my Model. Can I generate code from it?

Many thanks in advance!