A mail server does not have a user interface, it's a set of protocols which allow interacting with the server.

POP3

Its purpose is to check the incoming mail. Though a user might have many folders on the server, they are not checked, the only active folder is the INBOX one. The protocol is very simple and is supported by all e-mail clients. It allows retrieving a list of messages available on the server, you can see their size, either download, delete or leave on the server certain message(s). It is also possible to partially download messages, in other words the message header and a certain number of text lines.

IMAP

It also allows checking incoming mail, but offers a lot more additional features. It appeared mainly as the evolution of the POP3 protocol, almost all of the functions are shifted from the client to the server. This allows using the so called "thin" clients, that are primitive applications and all the work is done by the server.

The user can have quite a rich folder structure where the messages are stored. The server splits e-mails into several parts and you can gain access to any of it. For instance, you can download the attachment only. Unlike POP3, this protocol allows processing more than one message at once requesting only the needed information from the server. For example, you can request senders, recipients and messages' size for e-mails in the list from 5th to 10th inclusively.

It is possible to search for messages with quite narrow conditions, e.g. find all the messages from a certain sender for the last month.

Besides the protocol standards a lot of additional extensions were adopted increasing the protocol's capabilities even more. It all made IMAP4 very complicated and sophisticated. Not all the e-mail clients and servers support it, and what's more none of them really support all the protocol's features.

SMTP

It is used to send messages from users to the server and also for sending messages from one server to another. At the same time the sender's addresses and the addresses of the recipients are indicated separately for each of them. This allows returning an error message at any stage of the process. For instance, the server might refuse to receive a message from a given sender if such a sender address does not exist or if a recipient's e-mail address is not found.

Primarily, the SMTP protocol did not perform authentication, but the ever increasing amount of spam e-mails (unsolicited messages with mainly advertising content) made that feature necessary.

When messages are sent to the external addresses the SMTP-authentication is often required, otherwise there would be an good possibility for the delinquents to misuse the server by sending messages via that mail server (open relay). Instead of authentication the server can impose restrictions based on IP-addresses. For example, sending messages to external addresses is only allowed from within the internal subnet.

The mail exchange between the mail servers is usually carried out without authentication as in most cases different servers know nothing of each other. The only restriction is that the recipient-server has to be the point of destination (at least from the sender-server's point of view). There are exceptions when, for example, a small company makes use of the ISP's server as an intermediate server for sending out mail. In this case it is necessary to use some sort of authentication or impose some restrictions (e.g. base on IP-addresses).