Because the pitcher and catcher handle the ball so much, they get a bit of a break when it comes to making mistakes. This is done by recording some of their mishaps as wild pitches and passed balls, rather than errors all the time.
In simplest terms, a wild pitch occurs when a runner advances from one base to the next (or multiple bases) because of a pitch that was so high, low, or far away from the strike zone that the catcher could not handle it with ordinary effort.
Conversely, allowing a runner to advance on a pitch that should have been handled by the catcher with ordinary effort is considered a passed ball. Like hits and errors, who is at fault is determined by the official scorekeeper.