Feeder. All circuit conductors between the service equipment, the source of a separately derived system, or other power supply source and the final branch-circuit overcurrent device.
With a generator there is no service point.Service Conductors. The conductors from the service point to the service disconnecting means.
I call it an equipment bonding (grounding) conductor. Green in the sketch below.is the ground conductor between the generator and transfer switch an equipment ground or grounding electrode conductor?