They are run as two entirely seperate organizations.
Tom Colicchio is in both and I have difficulity believing they are run as two entirely seperate organizations.
Yup, I can confirm that as well.
You probably have correct and accurate inside information. Still, I would expect that they share certain things in common, like design and favored construction contracters. I would also assume that TC's has some influence over how the kitchen is run in both Craft and GT, which is rather important when considering health code violations.
Bottom is that I work rather close to Shake Shack and have eaten there a number of times. It's not bad, but not that good either. Not worth the hype or the line, which I think are the produce of a good marketing group and an unusual location. Try NY burger on Park Avenue South, it's pretty decent with less of a line and looks cleaner, at least to me. Don't know what the health department thinks. And I don't like the way Shake Shack gets its deliveries....