Hi Pilou, there is not really any special name for just any curve that may be drawn on a surface, that would just be called a "curve on surface" I guess.

An isocurve is a special sub-category of curves on the surface which is a curve associated with one of the U or V directions of the underlying surface. A surface is basically a continuous net of curves crossing each other in these U and V directions, and an isocurve is just one single one of that network. It's basically aligned with the surface's control point grid.

There is not any "natural" built-in method with NURBS for drawing just any arbitrary curve on a surface and then moving the curve around and having the surface follow - that can only be accomplished with a lot of special calculations.

The natural way that a surface is moved is by moving the surface's control points around - those are the most basic part of the surface's definition that can be altered directly.

- Michael