I see that if give as input 4 control points and I ask for a 3rd degree curve I get a 3rd degree Bezier curve. I do not understand which kind of curve GH is giving me if I input (e.g) 5 control points and I ask for a 3rd degree curve. How is that constructed? What choices is the NURBS module doing?

Hi Maurizio -
A Bezier curve is a single-span NURBS curve - that is, the amount of control points is the degree of the curve +1.
A NURBS curve with more control points than the degree + 1 is a multi-span curve.
For more information, you could look into the following: