No, in this context Autococker is the nickname for the design/shape of the screw thread at the end of your barrel that goes into your gun. It's the most common type, pretty much the industry standard and is used on all Dye, Planet Eclipse and Empire markers. There are other threads out there, for example Impulse, Angel, Spyder, Tippmann and so on but you don't need to worry about them
Smart Parts, Empire, Lapco, Dye, Planet Eclipse and many other companies make barrels in a variety of different threads. But, like I say Autococker is pretty much the industry standard and most common.
Why is it you think you need a new barrel or barrel kit? The one that comes with the NT is just fine.