Cosmic Background Radiation (CBR) radiation is Electromagnetic Radiation (EMR) detectable in all directions. Diffuse Extragalactic Background Light (DEBRA) means more or less the same thing.
Some terms by type of Electromagnetic (EM) radiation:
The same phrase, Cosmic Background Radiation, is occasionally used to mean specifically the CMB.
Analogous is the Cosmic Neutrino (ν) Background (CNB or CvB or Relic Neutrinos).
Cosmic Gamma Ray Background (CGB)
Cosmic Infrared Background (CIB)
Cosmic Microwave Background (CMB)
Cosmic Optical Background (COB)
Cosmic X-Ray Background (CXB)
Extragalactic Background Light (EBL)