these are examples and not actual scenarios
A Carrier group is out doin their thang in the middle of the ocean, then the chinese navy is all like "**** that ****" and attacks. CTTs will be working with OSs with tracking and analyzing the threat, jamming whatever radar they got and basically prevent the ship from being barraged by missiles (since missiles are wireless, we can actually stop them if they are simple enough). CTRs will collect all the intel from the CTT database from the attack and send it to command. CTT and CTR will do some direction finding, but CTTs also maintain, last summer, my NROTC Unit went on a carrier and we saw some CTT Waaaaaaaaaay up on the comms tower doing some work. ITs a very hands on job. But the benefit of CTR is that you are a shoe in (with a degree of course) with the NSA when you get out. CTRs are very multi platformed they can be assigned to subs, carrier wings, surface ships, shore commands, and even with some marine units. they are the ones who get the signals intel the IS and IOs need to do their job.
Former NROTC cadet, quit school, gained 100 pounds, once I lose it I want to be a CTT.