There is a difference, and it has to do with how property is formed and maintained. You can chose to believe that property is arbitrary but the nihilists in our forum in the past have tried the same tactic unsuccessfully.
You are ignoring the homesteading principle, and other key tenants of private property all together.
Let me ask you this. If a robber is caught red-handed in burglary. His actions are delivered to the local private authorities. The local authorities will behave in a manner that is most likely to please their prescribers(consumers). Do you think it is more likely that they will charge some form of punishment against the robber? Or against the home-owner who defended his home.
Private property is also not arbitrary. That alone is enough to crush your whole premise. Earlier you challenged someone’s beliefs on what property is. I now challenge you to do a review and critique of your own knowledge regarding property.