They all give access to the same extra stocking place for each player; who can put items there and retrieve them by interacting with any of the console later.
Normally, free players have 12 bank slots, Premium 24 and Legendary 48.
There are also 9 "shared" bank slots. All characters on the same account can access these 9 slots and it can be used to trade account bound items.
The Shared Bank slots can be extended to maximum of 24 with the Additional Shared Bank Slots token from the marketplace.