Squaring to bung is important; you will sometimes hear announcers talk about a “swinging bunt,” which is basically when a batter takes a swing (or most of a swing), hits the ball, and gets a weak ground ball out of it. The result isn’t necessarily that different from a bunt, but it’s not counted as a bunt, which is important for statistical purposes.

There’s a variation on this called the “wheel play” where, when the first baseman charges, the second baseman breaks to cover first.