A Premium Inboxes inbox is a Google Workspace or Microsoft 365 account, delivered with domains, DNS and warmup, and uploaded to your sequencer. That is the same kind of mailbox PureMail sells, and both send through Google’s or Microsoft’s own servers.
The difference is what each inbox is allowed to do and how you pay for it. Premium Inboxes caps each inbox at 15 cold emails a day. A warmed PureMail inbox sends about 30, so you need half as many inboxes, half as many domains and half the accounts to watch.
So Premium Inboxes vs PureMail is less about the mailbox and more about the maths: a lower monthly price, and twice the sending from every inbox you pay for.