The benefits paid for hospital services will depend on the type of cover you purchase and whether your fund has an agreement in place with the hospital in which you are treated.
When there is an agreement between your fund and your private hospital, you will have either no out-of-pocket expenses or you will be provided with details of your out-of-pocket expenses. Public hospitals don't have agreements with specific funds and generally treated as though they are agreement hospitals.
You are entitled to and should always ask your hospital or health fund for an estimate in advance of the costs of your treatment, in both private and public hospitals.
Day hospitals generally admit and discharge you on the same day. Night hospitals have the facilities to treat you for overnight stays.