A Curve is an object that is expressed in terms of mathematical functions, rather than as a series of points such as vertices. Use this tag for any questions pertaining to the "Curve" Object type in blender. Use this tag for questions about curve object types in Blender.
Curves and Surfaces are particular types of Blender objects. They are expressed by mathematical functions (interpolation) rather than linear interpolation between a series of points.
Blender offers both Bézier and NURBS. Both Bézier curves and NURBS curves and surfaces are defined in terms of a set of “control points” (or “control vertices”) which define a “control polygon”.
Curves at the Blender Manual