There are two parts when it comes to dealing with mails:
- Mail transfer
- Mail deliver
On a very simple level,
- Postfix (MTA, Mail Transfer Agent) transfers mails from your server to other servers, on SMTP Protocol (Simple Mail Transfer Protocol).
- Dovecot (MDA, Mail Deliver Agent) delivers mails from your server to Thunderbird (MUA, Mail User Agent), on IMAP (Internet Message Access Protocol) or POP3 Protocol (Post Office Protocol 3).