When you're talking about sleeping, there are several stages:

• When you're awake and then start sleeping, it's called "going to sleep".
• After you have gone to sleep, we say that you "are asleep".
• Then you "wake up".
• Once you wake up, you "are awake".

There are other actions that have similar stages. For example, you "put on" clothes, then "wear" them, then "take them off".