F-Droid (the service) is focused on providing apps that are compiled by them using the original source code (they can redistribute the developers' APK if the bu

F-Droid (the service) is focused on providing apps that are compiled by them using the original source code (they can redistribute the developers' APK if the build process is reproducible). F-Droid (the client) is simply a way to easily access the F-Droid repository (which is there out of the box), but anyone can create a repository and male it available to be registered in the F-Droid client as another source, completely independent from the F-Droid service.