Tactics Trainer vs Real Time...

What about Tactics Trainer vs. Blitz?

My tactics training rating and blitz rating are about the same, whereas my cc rating is much higher.

Obviously there is some correlation. The better you are at chess, the higher both ratings will be. The higher one rating is, the higher the other rating will be, provided that you actually take the time to play both. Obviously some Masters and other high-rated players will have low Tactics Trainer ratings simply because they don't bother with it. But if you forced everyone to play, the better you are at chess, the higher all of your ratings will be.

But as to a direct correlation, I doubt one will ever exist. The Tactics Trainer rating is not a real rating; it is simply a number that the program uses to feed you problems of an appropriate difficulty level. A 1600 score on Tactics Trainer doesn't mean that you were able to beat a bunch of players with an Online Chess rating of 1400s and 1500s and 1600s. It just means that you solved a problem that others with lower scores were not able to solve on a consistent basis. 

That is an interesting insight, about TT and blitz...

However, what is cc?

CC stands for Correspondence Chess. My blitz rating is an embarrassing 815 while my Turn-Based (CC) rating is shown above: 1570. Age accompanied with chronic illness could be at the root of this huge discrepancy. If chess.com's Tactics Trainer does not speed up my brain function, then I expect a full refund of my diamond membership!

I'm not complaining, as I am happy to be breathing.

CC has history behind it and I played it via the post office in the early 80's with one college friend who played jazz tenor sax on a cruise ship. I don't know why chess.com deviates from what I understand to be the more correct way of stating this type of chess. However, it doesn't bother me at all what it's called. It could be called "Really, Really Slow Chess", and that would also be fine.