Cosmic background radiation (CBR) is electromagnetic radiation (EMR) detectable in all directions, from beyond the Milky Way. Sometimes it is meant to represent EMR from a significant redshift, or even specifically from the early universe. Diffuse extragalactic background radiation (DEBRA) means more or less the same thing, but doesn't specifically imply cosmological distances. Some terms by type of electromagnetic radiation:
The term extragalactic background light (EBL) is similar but typically is meant to include microwave, infrared, visible light, and some ultraviolet.
Analogous are the cosmic neutrino background (CNB or CνB or relic neutrinos), the background of cosmic-ray particles, and the gravitational wave background (GWB).
The same phrase and abbreviation, cosmic background radiation and CBR, are sometimes used to mean specifically the CMB.