half asleep and half awake; trance
Describes a state between sleeping and waking, or a dreamy, trance-like condition. Often used in the phrase 夢うつつで.
I was so tired that I listened to the lecture half asleep.
She was in a trance-like state and didn't notice even when her name was called.
dream and reality
Refers to the boundary or mixture of dream and reality. Often used in expressions like 夢うつつの境 or 夢かうつつか.
I could not tell the boundary between dream and reality.
I felt as if I were wandering the border between dream and reality.