I came up with my own definition of 3D that I'll submit here for your consideration.
I believe 3D is any maneuver that to be performed requires the constant harmonized input of three or more controls simultaneously while the maneuver is taking place.
Using this I divided the maneuvers in two categories:
1) Quasi-static controls maneuvers:
Under the previous definition a loop, a roll and a 360 pirouette are not 3D. Those maneuvers are performed by simply leaving one control in a single spot to complete the maneuver with slight and precise modifications to compensate or correct for a perfect maneuver. Even if the maneuver requires several inputs such as in a cobra roll you do them one at a time. This doesn't mean at all that non-3D maneuvers are easy to perform. I actually believe that precise non-3D maneuvers require a very high level of sophistication from the pilot.
2) Dynamic controls maneuvers:
I consider maneuvers to be 3D as those where during the whole time while the maneuver is happening two or more controls are being changed constantly to achieve a smooth harmonized effect.
1) A piro flip requires constant moving of the elevator and aileron control in a circular stirring and synchronized fashion while at the same time rudder is kept at a constant rate while the pitch is being changed up and down constantly to prevent it from falling. 3 controls changed simultaneously.
2) A rolling circle requires constant traveling through positive pitch with a bit of left rudder then down to the middle of the travel, no rudder and at this point that the heli is in a knife edge position a bit of down elevator then negative pitch and a bit of right rudder and then back to the center on the left stick and again while in knife edge a bit of up elevator. 4 Controls simultaneously being changed
3) A piro loop requires precise control of the pitch so the model won't lose momentum while at the same time you need to rotate the right stick in syncronization with the heli's orientation to the loop plane.
Using these criteria some maneuvers that most people consider 3D such as a funnel wouldn't fall into the 3D category because they comply with the Quasi-static controls maneuver definition. Now if you take a static funnel and you make it into a morphing funnel then it becomes 3D because to perform it you need to constantly be changing three controls simultaneously.
By the same token, fast backwards flying used to require constant input to prevent the tail from weathervaning. Nowadays with the advent of heading-hold gyros this maneuver changed from a 3D maneuver to a non-3D maneuver.
The same way if instead of a 360 pirouette you start pirouette-flying around then you need to start moving the elevator, aileron and pitch to control the location you want to move the helicopter to and this at the same time synchronized with the heli's attitude towards the flight path.
Those are what I consider the difference between 3D and non-3D maneuvers.