If you are tired from working too hard then your body can recharge. Taking a weekend completely away from work can bring you back to normal. If your levels of exhaustion get worse then it can take longer. When a complete two-week break from work cannot undo the damage and bring you back to a normal level it is a sign that your body has adapted to a new level of normal.
I'm not sure that there is a real difference between burn out and depression. They probably overlap to some extent and share symptoms. I think that depression is caused by a lack of serotonin in the brain (hence SSRIs as an effective treatment). Burn out is caused by an inability to produce any more adrenaline; living in a state of constant stress has affected the bodies ability to produce it on demand and caused some kind of adaptation to its effects.
There are tests for determining stress levels in the run-up to burn-out that measure cortisone levels in the blood. Too high above base level can indicate the presence of too much stress. After burn out the levels collapse to below a normal base-line.