Baseball, by the Rules
A Foul Ball is Not Caught (but Should Have Been)
If a ball is hit in the air into foul territory, the defenders can attempt to catch that ball for an out. But what if they try to do so, and fail? Well, that could wind up being scored as an error. As with any error, the key is that the ball could have been caught using ordinary effort, and a fielder needs to at least touch the ball.
So, if a ball gets popped foul, the catcher and the third baseman race over to catch it, and then each of them thinks that the other has it, and it drops in harmlessly, that’s not an error; even though it was ball that could have been caught with normal effort, no one touched it. Similarly, if a long fly ball goes down the foul line, and an outfielder races over, dives, and has the ball tick off their glove in foul territory, that’s not an error, either; even though the defender touched the ball, it required a greater-than-standard amount of effort to even get to the ball. But, if everything comes together— the ball is hit foul, but well within the range of a fielder, and that fielder gets their glove on it but just plain drops it, that’s an error.
One thing makes a missed foul ball catch different from other errors: unlike other errors, which would allow an offensive player to reach base, take an extra base, or score when they otherwise would not have, missing a foul ball catch simply means that the batter gets to keep batting. There's no guarantee that the batter is going to reach base; as such, you might not see a missed catch scored as an error until the plate appearance is resolved; if the batter reaches base, the official scorer can say that the reprieve the batter got from the missed catch should go as an error.