Object Mode and Edit Mode
When adding curves there are some common options like other Objects.
In Object/Edit Mode, the Add Curve menu, provides five different curve primitives:
Adds an open 2D Bézier curve with two control points.
Adds a closed, circle-shaped 2D Bézier curve (made of four control points).
Adds an open 2D NURBS curve, with four control points, with Uniform knots.
Adds a closed, circle-shaped 2D NURBS curve (made of eight control points).
Adds a NURBS open 3D curve made of five aligned control points, with Endpoint knots and the Curve Path setting enabled.