(disclaimer, I'm a Microsoft employee and this is only my opinion).
There's an important distinction which often don't see discussed when this topic comes up: It can be very dangerous to install a program on your machine, but an 'app' comes with some assurance. People often think of the app store as a method for MS to grab your money, but in my opinion it fixes many of the installation/deployment problems that have existed on windows since... 95?
'Programs' typically require an MSI for installation. You'd better know, and trust, the MSI before you give it the required administrative privileges it needs to run, because a rogue MSI can absolutely own your machine.
On the other hand, 'Apps' declare what they are going to do to your machine via the manifest, so you kind of know what you are getting into before your install. The apps are sandboxed, so they have limited ability to tamper with your machine, and they can be uninstalled in a more uniform fashion.
In short, I feel much better telling my Grandma that she can install an 'App', but i'm much less confident telling her that it's ok to install a program via Installer.MSI.