The term stage 4 nightmare was introduced in or shortly before 1968 by the American sleep researchers Charles Fisher (1908-1988), Joseph V Byrne, and Adele Edwards It refers to a common type of night terror which may occur during the stage of deep sleep, characterized on the electroencephalogram (EEG) by delta waves. This sleep stage was formerly referred to as stage 4 sleep, hence the term stage 4 nightmare. The latter is traditionally used as a synonym for the term night terror. As noted by the American psychiatrist Ernest Hartmann (b. 1934), the choice of the term stage 4 nightmare is unfortunate, because it falsely suggests a connection with the *nightmare (which is regarded as different, in a conceptual and phenomenological sense, from night terror). The term stage 4 nightmare is used in opposition to the term * stage 2 nightmare.
References
Fisher, C., Byrne, J.V., Edwards, A. (1968). NREM and REM nightmares. Psychophysiology, 5, 221-222. Hartmann, E. (1984). The nightmare. The psychology and biology ofterrifying dreams. New York, NY: Basic Books.
Dictionary of Hallucinations. J.D. Blom. 2010.