To display only what you own, click the "owned" button (at the top of the window).
Coollector is basically a movie database that you can personalize by marking what you've watched and what you own, and as I said above, it takes only one click to show only those.
You'll soon realize that this concept makes things faster and less tedious, compared to the other apps where you have to add each movie one by one, after making an internet search each time. With Coollector, you can conveniently browse the database and mark what you own or have watched. The other advantage is that the app becomes a great way to discover movies and decide what to watch. There's an advanced recommendation system, and the filmographies contain all the movies a person has done (you can still restrict to what you own with a single click).
To summarize, Coollector is a great collection organizer, but its unique concept goes well beyond that.