The mall signed a property management fee with us instead of rent and management fee? What is the difference?

The rental fee is the right to rent a shopping mall/shop/booth. If you are the owner, you don't need a rental fee, which means you need to rent a shopping mall/shop/booth from the owner before you have the right to use it.

Property management fee (property service fee) is the fee required by property service companies to provide property services (some of which belong to management services) to public areas of shopping malls. Such as regulating parking, sanitation and cleaning, fire management, safety monitoring, public order, etc.