睡觉 means 'to sleep' e.g. 我想睡觉 I want to sleep. 睡着means 'sleeping' i.e. 他睡着-he fell asleep (and he is still sleeping) 着zhē (in this context) is used after a verb to show that the action is continuing, i.e. 听着(listening),看着(looking),等着(waiting) It functions like 在or 正在but they are placed before the verb and 着 is placed after the verb.

睡觉 = go to bed 睡着 = fall asleep

someone lies on a bed to have a rest, we can call that "睡觉"。 someone lies on a bed to have a rest without knowing what happened around, we can call that "睡着"。

我要去睡觉= I'm going to sleep 该睡觉了= It's time to sleep 他在睡觉= He is sleeping 他睡着了=He fell asleep

any difference between sleep and slept?