The difference between public and private listings is visibility.
While public listings are visible to every user/visitor, private listings are only visible to:
Guest list members
Guest list invitees
Visitors who follow the "share" link of your listing.
In other words, if your listing is private, it will not show up on searches or will not be reachable with a direct link unless the user/visitor has the share link or have been invited to your listing's guest list.
You can set your privacy option to "public" or "private" whenever you want from the listing setting menu.
You can find the "share link" in your listings main page. Anyone who follows the link will be automatically invited to the listing's guest list.