Exhaustion was an almost collapse of the body and mostly a sign for the person that the body needs recovery.
In 2268, Doctor Leonard McCoy diagnosed Spock with exhaustion caused by working too hard and guilt over crippling the USS Enterprise, thereby making their return to Amerind to rescue James T. Kirk and complete their mission there take longer. (TOS: "The Paradise Syndrome")
The Traveler experienced an exhaustion, when he brought the USS Enterprise-D far away from the Milky Way Galaxy in 2364. He recovered during his time in sickbay and was able to bring the ship home with the help of Wesley Crusher. (TNG: "Where No One Has Gone Before")