I see exhaustion and fatigue as two separate things. When I am not getting enough sleep, stressed, busy for hours and feel extremely tired, that is exhaustion.
However, fatigue doesn't have much to do with sleepiness to me. I can rest for hours and not feel refreshed.
It puts me in a very strange mental condition as well, I am no longer even able to feel tired or be aware that I'm tired, I just am tired. I don't know if that makes any sense.