Spline editing options are available through both multi-functional grips and SPLINEDIT. These options include add, remove, stretch, refine, and change the tangent direction. SPLINEDIT offers more editing options than the grips, but, to save time, the most commonly-used options are available in the grips.
In general, editing a spline with CVs allows you to reshape a small area of the curve, while editing the spline with fit points allows you to reshape the entire curve. Depending on the degree of the curve, the spline only changes through a given set of CVs and you can add more CVs to obtain greater control for a given area of the spline (the refine option). Mathematically, fit points affect the entire spline and force the curve to pass through specific points.