George There are some significant differences
1) In the quick stop, the head sail is dropped
2) There is no second heave-to in the quick stop
3) In the quick stop the pick up is usually on the windward side. I have seen some leeward pick ups.
Your downwind is trickier. All of the techniques are similar.. Get some distance between the MOB and the boat. Come about. Close reach / close hauled back. We then heave-to rather than luff sails.