The difference between the two is that the App Store version is "sandboxed" where as the standalone version is not.
"Sandboxing" means that the application is limited in what kind of resources on your computer it can access. This is the reason that when using the App Store version for the first time, you have to confirm the location of your OneDrive on your computer. This makes that folder available through the sandbox for OneDrive.
Sandboxing means that some features won't work on the App Store version - i.e. they're not available. However, Microsoft really isn't documenting or emphasising anywhere what those features might be. "Ordinary" home user usage of OneDrive is fully supported, but if you want to use other features, you might have to check that they work in the App Store version. For example take a look at this Microsoft guide:
It explains how you can set up OneDrive to synchronize files with an enterprise Sharepoint installation. As the first step it tells you to uninstall the App Store version of OneDrive, and install the standalone version.
In short: If you want all features, use the standalone installer. If you want an easy, familiar installation process - use the App Store version.
Only Microsoft can say why they decided to have two different installation options. In general however, the most common reasons for doing that is supporting enterprise automated installations, and for supplying "familiar" and "easy to use" installation for home users.