The reason I like "Control Coordination Exercise" is that it better fits the maneuver into the continuum between the student being able to coordinate the controls under fairly stable flight conditions (climbs & descents or take offs) and conditions where larger control inputs--and therefore more control coordination--are used (max performance take offs and autos).

The way I was taught it was to level-lower collective-flare-level and descend. This was taught as an Air Taxi/Quick Stop maneuver, but it's components are are a stepping stone to autorotations (including the same sight picture for the flare). Instead of making that connection though, that school's philosophy was to use it as a "quick stop", and the next step was that you'd be air taxiing somewhere and your instructor would start saying "wires...wires...wires..." (Which elicited reactions other than those desired usually.) I get the idea (it's the same way they'd do engine out/forced landing training) but completely misses what I think of as the main value of the maneuver. Supremo brings in something that I missed having trained under that philosophy: you can also throw in monitoring the RPMs, which provides an additional stepping stone to doing a good auto.

Anyway, those are my thoughts on it. If you haven't noticed, I run a web site to share and refine teaching techniques, and I've set up a page just for this topic.

Also, I'll throw in my practical application for the RD since it is a fun maneuver that you'll really use outside of flight training. This summer I flew with BoatPix for a few weekends, and the RD is all part of the routine. Catch up to a boat, RD, circle it, scoot on to the next. It's never a quick stop, but a very smooth, controlled maneuver that you use to position the aircraft. Finesse is key, since the Mariners we were flying are especially sensitive to being out of trim at high speed because of the big ol' floats they have on the skids.

This is how I set it up in my lesson plans;

Quick Stop:

Fly along the taxiway.  Just before reaching an intersection, say "quick stop".  The student "quickly", and "abruptly", "jams on the brakes"!  The point being to stop just before reaching the intersection.  (20-25ft / 40kts) (similar to a takeoff run)

Slow Down:

Initiate an Air Taxi to a specific point (compass rose, helipad, etc.).  Then slowely "tap the brakes" to transition from flight to a hover just above the LZ.           (50ft / 55kts)

Both of these maneuvers require the same coordination of the controls.  The "Quick Stop" is just done faster, and more abruptly.  I wouldn't call the transition to land on a cart, or truck a "Quick Stop".  But, then again, we're all pilots, and we can call these maneuvers whatever we want. 
 

In the teaching environment we should all be cautious of the words we use and how they maybe misunderstood. You’re correct in that the Quick Stop can be preformed with a quick and/or rapid cyclic application. That would then require an equally rapid application of collective and pedal to maintain coordination. The Quick Stop, in any case, is still preformed with smoothness and coordination.

There should never be any abrupt control movements, except in case of emergency. Abruptness is a sudden unexpected (unplanned) action lacking continuity.

http://www.youtube.com/watch?v=Z1rJ34kl0oo&feature=related

Lets define the terms:

Quick:

Moving fast or doing something in a short time; prompt; happening with little or no delay.

Rapid:

Happening in a short time or at a fast pace; characterized by great speed.

Abrupt:

Sudden and unexpected; not flowing smoothly; disjointed; lacking smoothness or continuity.

The FAA’s PTS sets the standard for training and testing in the U.S. As such, the PTS references the standards for the Rapid Deceleration in FAA-H-8083-21 (pg. 10-3), which calls for the maneuver to be performed slowly and smoothly with the primary emphasis on coordination.

COMMERCIAL PILOT 

Practical Test Standards

FAA-S-8081-16A, pg. 1-16

A. TASK: RAPID DECELERATION  

REFERENCE (S): FAA-H-8083-21; Helicopter Flight Manual.  

Objective. To determine that the applicant:   

1. Exhibits knowledge of the elements related to rapid deceleration.  

2. Maintains RPM within normal limits.  

3. Properly coordinates all controls throughout the execution of the maneuver.  

4. Maintains an altitude that will permit safe clearance between the tail boom and the surface.  

5. Decelerates and terminates in a stationary hover at the recommended hovering altitude.  

6. Maintains heading throughout the maneuver, ±5°.

http://www.faa.gov/training_testing/testing/airmen/test_standards/pilot/media/FAA-S-8081-16A.pdf

RAPID DECELERATION (QUICK STOP)

FAA-H-8083-21, pg. 10-3

In normal operations, use the rapid deceleration or quick stop maneuver to slow the helicopter rapidly and bring it to a stationary hover. The maneuver requires a high degree of coordination of all controls. It is practiced at an altitude that permits a safe clearance between the tail rotor and the surface throughout the maneuver, especially at the point where the pitch attitude is highest. The altitude at completion should be no higher than the maximum safe hovering altitude prescribed by the manufacturer. In selecting an altitude at which to begin the maneuver, you should take into account the over all length of the helicopter and the height/velocity diagram. Even though the maneuver is called a rapid deceleration or quick stop, it is performed slowly and smoothly with the primary emphasis on coordination.