Today I spent several hours doing hard, grueling, completely mindless physical labor. It's nowhere near my bedtime, but I'm physically exhausted, my back hurts, and all I really want to do is sit in bed until I go to sleep.
On other days, particularly at work, I do nothing but sit in a chair all day programming. I am not at that point physically tired, but I may become mentally tired due to the mental work I'm doing, stress of dealing with coworkers etc.
From this, I know that there appears to be a difference between the two types of exhaustion. One leads to me mindlessly walking around the office playing pokemon, and the other leads to me asking interesting questions on stack exchange sites that I've never been to before.
That being said (TL; DR)
Is there a recognized medical difference between physical and mental exhaustion?