What is the difference between "Screen On" and "Awake"?
This part of your screenshot you can find explained (partly) in my answer to What is Cell standby and how can I keep it from eating my battery?. But more specifically to your question, here's what it is about:


Network signal: Quality of the signal (colors are explained in this answer)
GPS on: Whether GPS was actively used
Awake: some app requested a Wakelock (see: How to deal with (orphaned) WakeLocks?). At least that's the best logical explanation to your question, though I cannot name a reference for that.
Screen on: the screen was turned on (either manually by the user, or automatically by an app). If the user turns the screen on, that doesn't necessarily mean a wake lock being aquired.
Charging: a charger was connected and supplied the device with energy