An apparatus in the form of an adapter for forming a connection comprising a first part adapted for coupling with a second part by a quick-release coupling formed by a first projection of the first part having an at least partial dovetail shape and a recess of the second part having an at least partial dovetail shape. An opening in the recess is adapted for receiving the projection in an axial direction. In other embodiments, the adapter is: (1) frictionally enhanced for engaging an internal portion of the drilling element; (2) includes a radial projection elongated in an axial direction for engaging the internal portion of the one drilling element; and/or (3) has a cutter for scoring an internal portion of the one drilling element upon being inserted therein and rotated. An adapter is also disclosed for use with a drill chuck, including for creating a “twist lock” connection.