The kind of electromagnetic radiation that arises from nuclear excitations is gamma rays. They are produced when an atomic nucleus drops from a higher-energy state to a lower-energy state, releasing the excess energy as a high-frequency photon.
Gamma rays are not defined only by their energy; their origin is important. X-rays can have overlapping energies, but they usually come from processes involving electrons outside the nucleus, such as electron transitions or rapid deceleration. Gamma radiation, by contrast, is associated with nuclear transitions, radioactive decay and other nuclear reactions.
A famous example is cobalt-60, whose radioactive decay leaves the daughter nucleus excited; it then emits gamma photons as it settles into a lower-energy state. Gamma rays are highly penetrating and can damage living tissue, but controlled beams are also used in medical cancer treatment, sterilization and industrial imaging. “Gamma rays” and “gamma radiation” are both standard terms for this phenomenon.