Nicholas Einhorn “Nicks’s flick” or Jean Pierre Vallarino “kick deal” as seen on World Greatest Magic: This is more like a fast top throw or push off with the index finger with a twist in the wrist. See Nicholas Einhorn’s lecture note “commercial magic 2000” for a complete instruction and a method for catching by using the first part of the swivel cut. The idea is the same as with the long distance shot done by the thumb.
Another version of the shot is Jean Pierre Vallarino “Turn kick deal”. Same as one before but now the card turns in midair. He does a slip cut and let the top card of the right hand pushed a bit to the right as he pushes and flicks his finger forward.