Account Vault: Net-7 Account vault is used to transfer items between linked E&B game accounts (9x game accounts can be linked to 1x net-7 account). This costs zero credits but the transfers must be done by toons (game characters) that are NOT logged in. Its not really a 'VAULT' but a way to quickly transfer items from one toon's in-game vault to another toons in-game vault. This can be setup via the Account tab on the net-7.org website. Most players use this method as its simple and you can just create toons to act as 'vaults' for ore, drops, ammo, etc without having to log them in to transfer items.
Team Vault (its been over 5 years since I tried this out so if any active users have additional info feel free to correct me): this is to transfer items between different Net-7 accounts and works the same way the account vault works but allows restricting access to those accounts, and toons, that you want to access it. It requires credit upkeep (5 mill to create and 15k per day, per toon that has access.....this can get expensive). Generally this is ONLY used by guilds, between trusted accounts, as anyone that has access can remove all items at any time.