Flash, it depends on how quickly over time AND distance the sudden rise in pressure occurs, and again for the sudden drop.
A bullet has a very sudden rise over a very small distance, holds that high pressure over the very small lenght of the bullet, then the sudden drop in pressure. We hear that as a 'crack'.
I suspect in Concorde's case there's a fairly large difference in distance & time - comparatively speaking - so there's a less 'steep' rise in pressure, a noticeable delay then a less steep drop in pressure leading to a double 'boom'.