Update - Out Now
Switch - https://ec.nintendo.com/AU/en/titles/70010000028644
Android - https://play.google.com/store/apps/details?id=jp.pokemon.pok…
iOS - https://apps.apple.com/au/app/pok%C3%A9mon-home/id1485352913
Original
Differences with Free and Premium - https://home.pokemon.com/en-au/premium/
There'll be a free month of Pokemon Bank on 3DS when this releases
To commemorate the release of Pokémon HOME, we will make Pokémon Bank and Poké Transporter available at no cost for a one-month period after Pokémon HOME is released. You’ll be able to bring Pokémon from various Pokémon series games using Pokémon Bank and Poké Transporter. Once you've got your Pokémon in Pokémon Bank, you'll then be able to move them to Pokémon HOME!
https://home.pokemon.com/en-au/move/
This is way more expensive than Bank which is $6.50 for a year though at least there is some free functionality.
Also Pokemon Go connectivity will not be there at launch.
$25 per year just to store Pokemon? With no functionality to trade them into any other games yet? What a rort.