Forwarding is the simplest: mail to info@ arrives in your Gmail, for instance. Each address costs $1.75 a month plus applicable taxes, up to ten addresses per domain.
A mailbox keeps your mail with us, 10 GB each, and you open it in any mail program. You send and receive from your own address. Each mailbox costs $4.10 a month plus applicable taxes. A domain has forwarding or mailboxes, not both.
Both run on one mail subscription per company, paid a year in advance, and work without a site too.
Your AI can read a mailbox for you, if you allow it yourself. It can then only read: it can't send, move or delete anything, and mail it reads stays unread.