In the USA we often call them graphite fly rods (a very broad term as we'll see later on), while in Europe, Australia, & most other countries these rods are called 'carbon fiber' (or fibre, as some spell it). Since I'm an American, I'll refer to them as graphite rods for this discussion.
Technically, graphite fly rods are made from polyacrylonitrate fibers that are bonded together with various resins, typically by heating, or cooking, them. Before the bonding (cooking) is done this raw material is called 'pre-preg". The pre-preg is made into flat sheets & rolled tightly rolled around a steel shaft, or mandrel, which is tapered - giving the rod it's taper. The mandrel is removed after cooking the rod blanks & can be reused to make many more rods.
Scientifically speaking, carbon fiber is a man-made synthetic material, where as graphite is a form of crystalline carbon which is naturally occuring. Carbon fiber is used to make all kinds of things from bike frames to golf club shafts to tennis rackets to walking sticks. graphite is found in pencils & used as a lubricate in powdered form. While both of these materials are carbon based, both are very different from each other - even though they have become interchangeable terms (at least in America).
As with a lot of other cultural things, we here in North America tend to have different names for the same things as other folks around the world - think: flashlight for torch; or car hood for bonnet, etc. If you've ever wondered what the difference was between carbon fiber & graphite fly rods - don't feel foolish for not knowing. It's just another example of differences in terms used in different countries.