An opamp is a particular circuit topology that was defined many years decades ago. There were, in fact, tube opamps. There are a small handful of topologies that are defined as opamps with a given, more or less well understood behavior.
Every chip opamp contains many devices on the silicon which make up the opamp circuit. Different chips have different quantities and types of devices depending on the specifics of the design, such as speed, current output, input device types, etc.
Since an opamp is a defined circuit topology made out of a collection of components, it's possible to make an opamp from discrete components. Most opamps are voltage feedback types (so far as I know), but some are current feedback circuits. The Carbon uses our design for a current feedback opamp amplifier.
Most chip opamps have very high open loop gain, somewhere near 120db (1 million). To reduce this gain down to 1X for a headphone amp requires a huge amount of global feedback (i.e., 120db). For this reason, I believe, many chip opamps sound ok for audio amps, but not usually really really good.
The Carbon discrete opamps have much lower open loop gain and, hence, the amount of feedback required to achieve unity gain is not so high. Hence, MHO, a better sound.
Just FYI, so far as I know nearly every solid state power amplifier that has ever been sold for the last 5 decades has been a discrete voltage feedback opamp.
See here for a good article on this. Note section 1, The Generic Amplifier Configuration
http://www.douglas-self.com/ampins/dipa/dipa.htm
