To convert a corner point to a smooth point, drag away from the corner point to make direction lines appear.
To convert a smooth point to a corner point without direction lines, click the smooth point.
To convert a corner point without direction lines to a corner point with independent direction lines, first drag a direction point out of a corner point (making it a smooth point with direction lines). Release the mouse button only (don’t release any keys you may have pressed to activate the Convert Anchor Point tool), and then drag either direction point.
To convert a smooth point to a corner point with independent direction lines, drag either direction point.