ExSimGuy has the right "generic" answer.
I have an account with Maglobe for when I'm globetrotting, and it has an authenticating SMTP server as part of the package. That account will work regardless of how I connect to the Internet.
The laptop also connects to the Broadband connection in the "main" and the "second" home - which use different ISPs. I've configured Thunderbird to show three different "sending" accounts: they all use the same "from" address, and put sent mail into the same "sent" folder, but they route via ISP1, ISP2, and Maglobe.
Unless the recipient bothers to examine the headers, they don't know which of the three I've used.