A Ball on a Wild Pitch/Passed Ball

The pitcher pitches, the batter takes, and the ball ends up somewhere other than safely nestled in the catcher's glove. One thing is very clear: the pitch was a ball. Whether it was a passed ball or a wild pitch is, in part, up to the scorekeeper, but it is also up to the runners on base. If they stay put, the pitch is just a ball. If they take off, things get interesting.

Once the defense recovers the ball, whichever fielder (usually the catcher) does so gets to decide if they have a play on a base runner. Many times, they won't really have such a play; if the ball gets far enough away, the runners will just take a base, and everyone resets afterward, with or without baserunners, depending. But if the defense gets a chance, they can always try to get an out, and the logic becomes exactly the same as you would see for a stolen base attempt.