Checking: an account that can be filled by the user and authorized to let other entities have access to on a case by case basis.
Example: User authorizes an email app to automatically deduct payments from the users checking account to send emails.
Savings: an account that can only be accessed by the user.
My concern is the average user will get tired and burnt out accepting every little transaction. This would allow the user to conviently have their account charged and prevent apps from draining a users account completely.