HBOMAX account within Apple + subscription?

Those are two unrelated subscriptions, and you do not need to use the same account (but it is possible). There is no “within”.

• HBO Max allows for in-app subscriptions on Apple devices, linked to your Apple ID account, with payments through Apple. That subscription would be valid on any of your Apple devices with the same account. You may need to “Restore Purchase” to have it recognized on secondary Apple devices.
• HBO Max allows for subscriptions started with HBO Max directly. This requires an HBO Max account, and any email would be registered in their records. This subscription and account would be valid on any supported platform.

To switch between these types of subscriptions, you will need to cancel on one platform, and re-subscribe for the other type.