It is very simple. If you chose appcenter (system-wide), the application will be available for all users on the system. But if you chose appcenter, the application you installed will be available for the current user only.
This is a good option in Elementary OS. So if you want to install some apps for a user, and not for the other users YOU CAN. The slogan “YOU CAN” is the best slogan for Linux community. Elementary OS just need more specific language to help users know the meaning of those words (appcenter and appcenter “system-wide”).
In Linux, YOU CAN customize everything if you will. In Linux, YOU CAN create your own distribution (operating system) if you will. In Linux, YOU CAN modify any open source software application / tool if you will. Linux is all about giving you the ability of “YOU CAN”. So I appreciate any feature added to any Linux distribution that makes people choose their way of usage in non-complicated way.