They are all the same.
Do bank runs cause recessions, or do recessions cause bank runs? Both. Neither. They are the same thing.
(This post isn't as clear as I want it to be, because my mind isn't as clear as I want it to be, so read at your own risk.)
I was making a second attenpt to read (as opposed to skim) John Cochrane's excellent paper "Toward a run-free financial system" (pdf). I got distracted at the top of page 8, where John says: