With preliminary classification, there are five behavioral functions for rapid eye movement(REM) sleep after puberty, which are memory retention, drive dissipation, muscular efficiency, heat control and adaptive immobility. For these diversities, it is newly suggested in this mini-review to categorize the REM sleep into two types respectively as atonic and brain REM sleep. In concrete words, the atonic REM sleep was acquired early in platypus, ostrich, and reptiles, responsible for the adaptive immobility as rare exceptions to predation risk of sleep, for the important function recently proposed for improvement of muscular efficiency in most species, and for the heat control in some species, while the brain REM sleep were added later in evolution, responsible for conflict of emotional memories against disinhibited drives. In ecological aspects, this division of REM sleep is useful to pluralistically understand the diverse adaptive functions of REM sleep in various species. On inductive relation, the atonia is required for EEG activation from brain stem in REM sleep, consistent with the earlier origin of atonic sleep in evolution. On physiological paradox, the pathological high muscle tension in human depression results from the emotional stress from accumulated emotional memories processed in long REM sleep, therefore not contradictory with the atonic function of REM sleep. On stage interactions, these two types of REM sleep are different as coherent and counteractive with SWS respectively. In these respects, the REM sleep plays two types of qualitatively different functions in the atonic and brain REM sleep respectively.