Public events are those listed in the "Upcoming events" on which Partyaner users can click to read more about the event.
Private events are those showed in the calendar but not listed in the "Upcoming events" so the Partyaner users can't click to read more about the event. This is useful when you want to make a private event(s) and let everyone know that you aren't free for bookings on certain date(s). Managing the private events is for free.
Read How to make a custom (private) occupations for more information.