In that particular screenshot I believe you’re right: the one on the left is Firefox ESR while the icon on the right is whatever flatpak version available.
But I know what OP is referring to as it is a open bug currently, the DE don’t doesn’t recognize the launched instance as the pinned program due to the way Flatpak launched apps. Not an issue with Firefox in particular
Flatpak integration is still not great (lemmy.world)
Its even worse when you force Firefox to use wayland its icon doesn’t even show....