all apps built for one distro can be run on another.

Pfft no. They won’t even work on earlier versions of the same distro. Or later. Or any distro where you’ve installed a library or driver thats older or newer than the one needed for the app your installing.

So in essence there is no difference besides the installation process, gui, and package manager.

There are three different package systems (Red Hat, Debian and Arch) and they are all completely incompatible with each other, and earlier versions of themselves. You can use containers like Snap or Flatpack or half a dozen other standards, which again are all incompatible with each other, and all of them except Snap aren’t fully containerised either - they are dependent on specific libraries and drivers in the distro.