Electromagnetic radiation has both wave and particle character. The higher the frequency f, the more pronounced is the particle character. The quantum of electromagnetic radiation is called photon. It has zero mass, an energy E = hf and a momentum p = E/c = h/λ, where h is the Planck constant, c is the speed of light and λ is the wave length of the radiation. The photoelectric effect, for example, is explained by the fact that light carries energy in discrete quantized packets, the photons.
In vacuum, photons travel at the speed of light; in matter, the speed is smaller.
Conventionally, electromagnetic emissions from excited nuclear states are called gamma rays, whereas electromagnetic transitions between low-lying atomic shells are called x rays. Usually – but not always – energies of gamma rays are higher.
(text contributions from Helmut Paul, 2014)