vs
QUICK ANSWER
"Overslept" is a form of "oversleep", an intransitive verb which is often translated as "quedarse dormido". "Asleep" is an adjective which is often translated as "dormido". Learn more about the difference between "asleep" and "overslept" below.
asleep()
An adjective is a word that describes a noun (e.g., the big dog).
1. (sleeping)
a. dormido
The baby was asleep before dinner ended.El bebé estaba dormido antes de que terminara la cena.
2. (numb)
a. adormecido
I was sitting in a weird position and now my foot is asleep.Estaba sentando en una postura rara y ahora tengo la pierna adormecida.
oversleep()
An intransitive verb is one that does not require a direct object (e.g., The man sneezed.).
1. (general)
b. no despertarse a tiempo
Martin didn't hear the alarm clock and overslept.Martín no oyó el reloj despertador y no se despertó a tiempo.