You cannot share games with different users on different consoles, the account and console need to be activated as a primary ps4 for this to work. Also you are able to move individual games if your format an external HDD from within the ps4 in order to play them directly from the external drive. The license is still for the same account holder.
The back feature is mainly when you want to change the internal drive or do a fresh format of it. Not to actually share data.
Again, data/games on PS4 are subject to DRM and are locked to the activated console and account holder. You are able to use the account on multiple consoles but then you will need to log in to the licensed account to play the game (the one who bought it basically).
PS4 External Storage
Activate PlayStation 4 System as Your Primary PS4