Typical mail server installations in a small network will probably use a single server handling POP3 and SMTP protocol ie drop box and mail server. Since it's a single server, a simple name like mail.example.com will be assigned to it and it responds on the appropriate ports for both POP3 and SMTP.
Huge networks may have a bank of servers running POP and another smaller portion running SMTP. Reasons for splitting this up are manifold, but SMTP servers are store and forward machines that pass traffic, POP servers in this day and age are also HTML interfaced and so you need quite a bit of disk storage for your user accounts as mail accumulates in their boxes since they no longer use the system as a drop box forwarding to a local email client. Under these situations, you assign all the SMTP traffic to smtp.example.com and the POP3 is given pop.example.com
In the case where a hosting provider has set up all three host names (mail, pop, smtp). you will probably see the mail.example.com address as an A record which has been CNAMEd to pop and smtp. They're all using the same IP address for the mail services, so for simplicity, I always just use mail.example.com. On a single machine, it's the ports being contacted that make the difference.