Some further color.
The T-1s and T-38s at Randolph are for teaching instructor pilots how to instruct students for advanced pilot training. The T-1 is for the bomber, tanker, and cargo/pax advanced traning, the T-38 is for fighter advanced pilot training.
The T-6s are for basic pilot training and those instructors also learn at Randolph.
Randolph used to have the 737s that were used for Navigator training (callsigns GATOR... get it, naviGATOR
) but those have since relocated to, I believe Pensacola FL. It was a multi-service mission so that explains USN involvement.
You will also hear multi-national training occurring at Randolph - squadrons will host IP students from multiple nationalities.