This is not nutrition but is of interest, at least to me.
Burnout and prolonged fatigue are both characterised by the symptom of fatigue. Both come from different backgrounds. Prolonged fatigue has a medical cause. Burnout has a psychological origin eg work conditions .
There is considerable overlap between the two conditions. However burnout is seen as not merely fatigue bu rather a specific work related syndrome.
Leone et al 2007 Similarities , overlap and differences between burnout and prolonged fatigue in the working population QJM vol 100 , 617-627