Storage Rooms are an access point to the pocket dimensions that your base's Storage Containers also use; so the inventories will be the same, based on which of the 10 numbered pocket dimensions you are accessing.
These rooms will unlock in your build menu one at a time. Place 0 to unlock 1, place 1 to unlock 2; etc.
The legacy freighter storage rooms look almost identical; but will no longer show your stock in tabs on your freighter screen. To access that feature again, players must delete them & rebuild as the new versions; which are aesthetically only mildly different.