That is a pretty good description of "event work".
I watched an interview with David O'Russell (I think it was one of the THR roundtables) about shooing The Fighter where he said that he was running around with the DP and camera op and just grabbing atmosphere shots of the town they were shooting in. Guys playing cards, kids playing etc.
I'd call that run-n-gun. I wouldn't call it event work.
It's fair to say that the majority of event work is shot that way, but I just shot a bunch last month on risers and sticks with house power and an xlr off the board for an event. And that was not run-n-gun by any stretch.