MLB - "appeal" vs "challenge"?

On a ball/strike call - the batter or the catcher (pitcher as well?) can “challenge” the call - losing the challenge costs the team a challenge. Who can “appeal” a call (usually to the 1st or 3rd base umpire)? If you can appeal - why waste a challenge?

Appeals are only to challenge if a batter’s swing counts as a swing, or was checked in time to not be a swing.

Also, an appeal of a swing/no swing call can only be made by the catcher or team manager.

Not the batter?

Nope. A batter can challenge a ball/strike call, but only a catcher can ask for an appeal to the 1B/3B umpire. The home plate umpire doesn’t have to grant that appeal, but they generally do.

In Bouton’s Ball Four, he recounted a spring training experiment where the batter could request an appeal to first or third if the home plate ump ruled the batter did swing. They abandoned it because the base umps invariably confirmed the home plate ump’s judgment.

That’s interesting. I’ve seen batters do it, but I guess it’s a useless gesture. I know the 1st and 3rd base umps don’t do anything until the homeplate guy asks for it.

And there is no limit to appeals. Mostly because it doesn’t happen frequently enough for there to be limits imposed.