What is the little badge on app icons in the All Apps grid?

Short answer: The badge shows whether each app currently lives on your Mac's built-in drive or on your fast drive. The Moved tab lists only the moved ones.

It shows where the app lives right now — on your Mac's built-in drive or on your fast drive. That lets you see at a glance which apps you've moved, while still opening every app from the same grid.

For a list of only the moved apps, open the Moved tab.