The Property is the building itself. Its physical characteristics, location, total space, # of floors, etc.
The Listing is the agreement you win to sell or lease that building.
As a Listing Broker you would create both records, but track all of your outbound marketing/selling efforts and inbound inquiries against the listing. Again this helps you for reporting purposes, and ensures everything is tied to one common record.
There is an exception here. If you are a Land Broker, and you are on an AscendixRE Land trial, we have co-mingled the Property and Listing tabs, so that you are managing all of your listings, within the Property record itself.