I was trying to set up thunderbird at home, but I am not able to send mail through SMTP server smtp.cs.arizona.edu. Are the settings different when sending from off campus as opposed to on campus?

You'll have to use whatever SMTP server your ISP provides -- unless your machine name ends in "cs.arizona.edu", you won't be able to send mail through smtp.cs.arizona.edu. So if you're on earthlink, for example, you'd use "smtp.earthlink.net" as your SMTP server. Check with your ISP for the exact name of their SMTP server.

For a more complete explanation of SMTP server possibilties see FAQ:

http://faq.cs.arizona.edu/idx.php/9/071/Email/article/Sending-email-from-CS-campus-and-elsewhere.html