What's the phrase for the time difference between waking up and gaining full consciousness?

Question

I think it starts with "sleep". It's not technically a disorder. As an example, let's say the phone rings. You become immediately aware of the phone ringing and you answer it, but there's a delay between when you answer the phone (consciously) and realize you're awake and thinking. What's that time gap called?

Answer 1

twilight

Answer 2

Two cigarettes and a cup of coffee.

Ob1