What storage expansion actually works, by console
Getting this asked a lot now so putting it somewhere findable.
On PlayStation you can add an internal drive of the correct type, or use external storage for archiving only. On Xbox the official expansion card is the simple route and external drives again only archive.
The thing people get wrong: external drives cannot run current generation games on either console. You can store the game there and copy it back, which is faster than downloading again but is not the same as installing to it.
Anyone with a correction, post it and I will edit.