Public and Private Inboxes are different but both should offer a way for anyone else that is sending you a DM or a reply to post in there. So, if the relay you are using requires payment to post, you will never see any DMs or replies. 

PUBLIC INBOX: You will receive a copy from clients that operate in the Outbox model. Primal, Damus and, to some extent, Amethyst do not send it yet. But they will soon. Coracle, for instance, will sends it there. 

PRIVATE INBOX: Amethyst, 0xchat and Coracle do send to your Private Inbox relays. 

inbox.nostr.wine allows you to pay to receive DMs from everyone else. So, having to pay here is not an issue because you are paying for the others. 

Each relay is different. 

 

 Bookmarked and zapped. I'll be coming back to read this multiple times 🥴🤔🙂