Why does hashing a file that includes user passwords make more sense than encrypting the passwords in that file?

It is not the same thing as having an encrypted password database on your computer if you have a file where you keep hashed passwords, but what exactly is the difference between the two?

Why is hashing superior to encryption when storing a passphrase in a file? The function and usage of a password file are both explained.

If you have a file where you save hashed passwords, that's different from having an encrypted password database on your computer, but what is the difference?