This looks like to me that you might have flatpaks installed in your home on the second laptop, while all your flatpaks must be installed system wide on the first one.
You can see what is installed system or user side with
flatpak --user list
flatpak --system list
As for the additional directories purpose, app contains the apps (surprising i know), runtime the runtimes needed by the apps (such as say the org.kde.Platform for kde apps etc), exports the things that are exported for integration (like a bin dir you can add to PATH or the applications dir containing the .desktop files to launch apps from the desktop etc. appstream is a metadata format about apps i’m not sure exactly what they put in that dir, some cache maybe ?
This looks like to me that you might have flatpaks installed in your home on the second laptop, while all your flatpaks must be installed system wide on the first one.
You can see what is installed system or user side with
flatpak --user list flatpak --system listAs for the additional directories purpose, app contains the apps (surprising i know), runtime the runtimes needed by the apps (such as say the org.kde.Platform for kde apps etc), exports the things that are exported for integration (like a bin dir you can add to PATH or the applications dir containing the .desktop files to launch apps from the desktop etc. appstream is a metadata format about apps i’m not sure exactly what they put in that dir, some cache maybe ?