REM sleep vs rapid eye movement

REM sleep and rapid eye movement both are nouns.

Word	Noun	Adjective	Verb	Adverb
REM sleep	Yes	No	No	No
rapid eye movement	Yes	No	No	No

As nouns, REM sleep and rapid eye movement are synonyms defined as:

REM sleep and rapid eye movement: a recurring sleep state during which dreaming occurs; a state of rapidly shifting eye movements during sleep

Other synonyms of REM sleep include paradoxical sleep, rapid eye movement sleep, REM.

REM sleep (noun)	rapid eye movement (noun)
a recurring sleep state during which dreaming occurs; a state of rapidly shifting eye movements during sleep	a recurring sleep state during which dreaming occurs; a state of rapidly shifting eye movements during sleep