Cosmic background radiation (CBR) radiation is electromagnetic radiation detectable in all directions. Diffuse extragalactic background light (DEBRA) means more or less the same thing.
Some terms by type of electromagnetic radiation:
The term extragalactic background light typically is meant to include microwave, infrared, visible light, and some ultraviolet.
The same phrase, cosmic background radiation, is occasionally used to mean specifically the CMB.
Analogous are the cosmic neutrino background (CNB or CvB or relic neutrinos), the background of cosmic-ray particles, and the gravitational wave background (GWB).