How email's mostly used now is way different from how it originally worked. SMTP used to be something email servers used to push email to other email servers, not something clients used.
Client A would dial directly into a shell on server B, and send a message, ultimately, through
sendmail, which talks directly to the server's own mail-transport agent(MTA). If the destination was on the same server, the email would be directly transferred to the recipient's
maildir folder without any networking required at all. If the destination was on server C, the MTA would eventually need to open an SMTP connection elsewhere to transfer it. (It needn't do so instantly. It needn't do so directly, either. It might send to server E, which would forward to server C, etc.) Client D would dial into server C and check their local
maildir folder for files to see if any mail had arrived.
In short, commandline mail didn't
use an SMTP server -- commandline mail
was an SMTP server. That's mostly how it remains.
Once home computers started getting network access, users were able to access POP and SMTP and IMAP to get mail remotely instead of directly shelling into your mail server, but the design of UNIX MTA's still reflects having local mail for local users.
There's lots and lots of different MTAs now. With few exceptions, they all look the same on the surface -- they all give you a commandline
sendmail program to send mail with, etc. Many of them still even use configuration files based on ones the venerable
sendmail server used -- even though their capabilities can be radically different. I suspect that's why trying to configure an MTA has involved so much brain damage for me. Others have suggested that the damage was there already
If all you want to do is have
sendmail forward to existing email addresses somewhere else, I wouldn't bother setting up a full-fledged MTA.
ssmtp is a tiny sendmail replacement which doesn't do any MTA duties at all, its sendmail command directly connects to remote SMTP servers of your choosing, like an ordinary email client would.