(Disclaimer: Not a native speaker, probably some weird grammer/syntax)
I don't know if what i had qualified as burnout, but these past three year i sometime felt mentally strained, with huge sleeping needs (but difficulty to get asleep), low motivation, low productivity at work and at home (and therefore more stress/mental strain).<p>Two years ago, tried to take vacations, did some sport (this one somehow helped, but not as much as i needed, and couldn't get motivated to do my best). I ultimately took a month leave and took my old student job, summer camp counselor, for two week. It worked.
Around last month, i felt the same, but couldn't take a long leave. My father (film set designer/decorator/constructor) was working on the set of a feature movie. i took four days (long weekend) to help him. Woke up every day at seven, did some woodwork, put some wallpaper, nailed/screwed some planks, went to secondhand market/junk shop with him, carried old furniture from there. I honestly don't know if it's the work i did or the fact that did it with my father, but it has been i long time i never felt this good.
So my advice: find a work you can do that's time consuming, physical, that you find meaningful, and do it with someone you like spending your time with. Maybe juste one of these will suffice, i really don't know.
For the last question, in my experience, it's both.