In a script module you write a program in Lua language and it is naturally executed by the Lua interpreter. The input and output pins have to be defined with a special syntax.
Also a series of Aximmetry specific functions and data types is added to Lua to handle vectors, colors, matrices etc.

While in an Expression module you can only specify a numeric expression which is internally translated into a graph of arithmetic nodes of Aximmetry.   For e.g.  if you type   a + b * (something + sin(other_thing)) the used variables will appear as input pins,  and internally the expression is translated into a series of Add, Multiply and Sine modules.

I'll send you some examples / documentation soon.

Please install   https://mab.to/6YY2mJPDC

You'll find some script and expression examples in [Common]:Tutorials\Scripting

Also there're older examples for special subsystems:
[Common]:Tutorials\Instancing\Instancing - 03 - Script.xcomp
[Common]:Tutorials\Particle System\Particle System - 08 - Script.xcomp

Special data types and operations are added to Lua for handling of VectorN, Matrix, Color data types of Aximmetry.
You can find their definitions in  c:\Program Files\Aximmetry\resources\plugin\lua\Math