paradoxical sleep vs rapid eye movement sleep

paradoxical sleep and rapid eye movement sleep both are nouns.

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

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

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

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

paradoxical sleep (noun)	rapid eye movement sleep (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