Humans have 5 stages ofor sleep, stages 1,2,3,4,5 . They don't really have specific names , but for example stages 1 and 2 are typically characterized as "light sleep" Stages 3 and 4 are "Middle sleep" and part of 4 and 5 are REM. Part two of your question is REM (Rapid Eye Movement) which occurs in stages 4-5.
I recently did a speech on this Topic! Let me know of you don't understand ! I hope this helps! :)