Gamma rays are the highest-energy form of electromagnetic radiation, being physically the same as all other forms (e.g., X-rays, visible light, infrared, radio) but having (in general) higher photon energy due to their shorter wavelength.  Because of this, the energy of gamma-ray photons can be resolved individually, and a gamma-ray spectrometer can measure and display the energies of the gamma-ray photons detected.
Radioactive nuclei (radionuclides) commonly emit gamma rays in the energy range from a few keV to ~10 MeV, corresponding to the typical energy levels in nuclei with reasonably long lifetimes.  Such sources typically produce gamma-ray "line spectra" (i.e., many photons emitted at discrete energies), whereas much higher energies (upwards of 1 TeV) may occur in the continuum spectra observed in astrophysics and elementary particle physics. The difference between gamma rays and X-rays is somewhat blurred. Gamma rays are always from nuclear energy level transitions of atoms and are mono energetic, whereas X-rays are electrically generated (X-ray tube, linear accelerator) and have a broad energy  range.