Is the term "nuclear electrothermal" recognized as referring to a specific type of propulsion technology (specifically, the nuclear thermal rocket with heat engine and arcjet afterburner)?
Nuclear thermal propulsion and nuclear electric propulsion are distinct concepts. In nuclear thermal propulsion, a nuclear reactor is used to directly heat the propellant. The heated propellant exits the vehicle through a nozzle to generate thrust.
I'll discuss electric propulsion in general before addressing nuclear electric propulsion. Electric propulsion is a broad class of non-chemical propulsion where electricity is used in some form make the propellant exit the thruster at a high velocity. The electricity needed to power electric propulsion can come from a variety of sources such as solar arrays, batteries, or fuel cells. With nuclear electric propulsion, the electricity comes from a nuclear reactor that generates electricity.
Electrothermal propulsion is a subclass of electric propulsion. Electricity is used to heat the propellant. (The exhaust can be relatively cool in other kinds of electric propulsion.) Arcjet thrusters are one kind electrothermal propulsion. Resistojets are another kind of electrothermal propulsion. The Variable Specific Impulse Magnetoplasma Rocket (VASIMR) is also typically classified as electrothermal propulsion.
Finally, nuclear electrothermal propulsion is simply electrothermal propulsion where the source of the electricity needed to drive the electrothermal propulsion comes from a nuclear reactor that generates electricity.