You sound a bit confused... Are you trying to send the mail from or to the e-smith server?
If you're sending mail from the e-smith to somewhere else, the built-in SMTP server (outgoing mail) will only allow users on the LAN to send mail through. As was stated before, there's no authentication on SMTP. If you open it up to the outside connection, ANYONE can use your server to send mail. Having an "open relay" server like this will get the server put on lists, and some servers will automatically reject mail from this list of servers. See
www.orbz.org or do a Google search on "open mail relays" for more info...
If you want to send mail while connected from outside your e-smith, you should use the SMTP server of whatever ISP you're using, like mail.aol.com or whatever. Most ISPs' SMTP servers are closed (just like the e-smith's), so they will only work when you connect through their service. In other words, you couldn't use mail.localisp.net to send mail when you're connected through AOL.
In short, SMTP is totally separate from your domain name mail. It won't change the email address or anything. It's just the server where the email starts its trip across the internet. To keep spammers out, most SMTP servers only allow local users (on the e-smith's LAN or the ISP's network, etc.) send mail. If you don't have access to an SMTP server from your ISP or whatever, and really need to send mail from outside the e-smith, you can get packages that allow you to check your email (with your username and password) via POP3, then allow you to use SMTP once you've successfully authenticated with POP3.