How to know an application is installed from google play or side-load?

And FYI apparently the latest version of the Amazon store finally sets PackageManager.getInstallerPackageName() to "com.amazon.venezia" as well to contrast with Google Play's "com.android.vending".

The PackageManager class supplies the getInstallerPackageName method that will tell you the package name of whatever installed the package you specify. Side-loaded apps will not contain a value.

EDIT: Note @mttmllns' answer below regarding the Amazon app store.