The App Store install what you would install through .dmg or .pkg. This is, if you install, for example, Android Studio, Docker and UTM, you will have three QEMU executables, one for each app.
Homebrew does quite a good job as a package manager for Mac, however, it's far from how the package managers work in Linux distros. For example, by running ``sudo pacman -Syu`` I upgrade everything that is installed, including the kernel, standard libraries, Python packages, language packages, manpages and so on. In Mac, I have to upgrade the system through system updates, homebrew packages through ``brew upgrade``, Python packages through pip, the App Store installed stuff through App Store and the manually installed apps through whatever the way they are upgraded.