Your @tamu.edu address is a forwarding address, not an actual mail box. Your @neo.tamu.edu address is a real mail box where mail gets delivered.
You can set up your @tamu.edu address to forward to any mail box you choose such as your @neo.tamu.edu, departmental email, Gmail account, etc. You can easily change where your mail is delivered by going to Aggie Computing Gateway and clicking "Edit Directory". If you wish to publish your email address (for example, in the Campus Directory), you should use your @tamu.edu address. For additional information, see Editing Your Directory Information.
Your @neo.tamu.edu is your mail box on the campus email system. For students, the university sends official mail to this account. Students are no longer allowed to forward mail sent to their @neo.tamu.edu address. At this time, faculty and staff have been able to forward their @neo.tamu.edu mail to another account such as a departmental email box.
For those who did not receive a TAMU Email account, any mail sent to your @neo.tamu.edu address will continue to be forwarded for the time being to the address that you designated, such as your @tamu.edu address. We highly encourage you to transition away from using your @neo.tamu.edu address.
In Traditional Neo, users were also able to create extra address names or "aliases" for their @neo.tamu.edu account that also delivered mail to their mail box. These aliases still exist and continue to work in TAMU Email. However, users can't edit or change them at this time. Note: For students, official campus mailing lists use your_NetID@neo.tamu.edu, not any of your aliases.