OK...so Aggies are from A&M, but not all from A&M are Aggies? That about right?
No, no ... if you attended A&M, you're an Aggie. Your blood is maroon, and you despise Tea-sippers. You are the 12th Man at the games --- you never sit down, you get kissed when the team scores, and, for some reason, you bend over a lot and cheer in strange tongues.
If you attended UT --- University of Texas, never-never-NEVER "Texas University" --- you're a Longhorn. You "bleed orange," and you tell hideous Aggie jokes. You flash hand signals that, in some cultures, are considered to be the sign of the devil (remember when Laura Bush was accused of casting a curse when she flashed a horn sign at someone during the first Inauguration?)
Have you met an Aggie up yonder? If they're an Aggie, ask them about College Station, and watch their faces light up!
Once an Aggie, always an Aggie. And yes, all A&M students are Aggies. You can never be a ex-Aggie, rather you become a former student.