Publishing a listing means that it’s approved, once you publish it, the user will automatically receive an approval email. Deleting a listing means that it’s rejected, in this case, the user will receive a rejection email.
The “Verified Listing” checkbox is separate from the approval process. It’s used to mark listings as verified, indicating that they come from a trusted vendor and give them more visibility.
I really thought that the verified flag was supposed to also block the listing from being display even after publishing, I kinda remember that it was acting this way before the last update but I guess I was wrong.