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Cosmic background radiation (CBR) is electromagnetic radiation (EMR) detectable in all directions, from beyond the Milky Way. Often, what is meant is specifically the cosmic microwave background (CMB), but the term also naturally refers to any such EMR. Sometimes it is meant specifically for EMR from a significant redshift (i.e., a cosmological distance) or even specifically from the early universe. Diffuse extragalactic background radiation (DEBRA) means more or less the same thing, but with less explicit implication of cosmological distances. Some terms by type of EMR:
Other than the CMB, they generally consist of radiation from the intracluster medium (ICM) and from many distant unresolved and extended sources, and some would not use cosmic for those. The term extragalactic background light (EBL) is similar but typically is meant to include microwave, infrared, visible light, and some ultraviolet. Analogous backgrounds are the cosmic neutrino background (CNB or CνB or relic neutrinos), the background of cosmic-ray particles, and the gravitational wave background (GWB).