What is the difference between REM and non-rem sleep?

Night and Day. Rem refers to rapid eye movement sleep and non-rem refers to sleep that is not rem. Non-rem is further divided into n1, n2, n3 stages where n3 refers to the deepest stage. Rem is usually when we dream and has similarities physiologically to being awake. We cycle through these different stages about every 90 minutes of sleep.
Different levels. Rem (rapid eye movement) sleep is associated with dreaming and usually occurs at the lighter levels of sleep later in the sleep cycle. Non-rem sleep occurs at the deeper levels and is usually not associated with the dream state.