Coordinate Spaces

Understanding Coordinates

The picture explains how spline's coordinates are calculated. Note: included Math component always work with world coordinates.

Local Transformed Coordinates

Local coordinates are not affected by any transformations and corresponds to real world coordinates you see in the Editor only if no transformation is applied. There are also LocalTransformed positions, which returns local coordinates with all transformations applied. For example,
        //assuming there is a spline with no parent and at least one point
        //set spline's position
        curve.transform.position = new Vector3(1, 0, 0);
        //scale on X axis
        curve.transform.localScale = new Vector3(2, 1, 1);
        //set local position (which is not affected by spline's transform)
        curve[0].PositionLocal = new Vector3(1, 0, 0);
        // = (3,0,0)
        print("Point's World Pos=" + curve[0].PositionWorld);
        // = (1,0,0)
        print("Point's Local Pos=" + curve[0].PositionLocal);
        // = (2,0,0). Local transformed is affected by spline's scale
        // and shows the "real" local position you see in the Editor
        print("Point's LocalTransformed Pos=" + curve[0].PositionLocalTransformed);