To the extent that there is any confusion here, I think that's just a matter of semantics. It seems to me that you've got a pretty good handle on the mechanics of the situation. Here's a way of defining things that I find expedient:
I consider the "diaphragm" to truly be just the diaphragm. No chords, no collectors. If a diaphragm has only one source of external shear resistance in which to dump the direct shear component of the applied load, then it is a cantilevered diaphragm. If there is more than on source, then it is a simple spanning diaphragm (or perhaps continuous multi-span).
Every differential element within a diaphragm has complementary shears on all four sides. At the boundaries of the diaphragm, as I've previously defined it, those shears need to dump into something. At the location(s) of direct shear resistance, the shears dump into the collectors. At the boundaries running perpendicular to the load, the shears must dump into something as well. And that something is what I deem to be the "chord".
The chord itself needs to be prevented from translating along it's own axis of course. However, where that resistance is supplied doesn't, in my mind, change the chord's primary function. In a cantilevered diaphragm, the resistance could be supplied at the tip of the cantilever, the base of the cantilever, anywhere within the span of the cantilever, or even somewhere beyond the span of the cantilever. None of this affects the diaphragm proper. Nor does it affect whether or not there will be a "chord". Defined this way, there's always a chord.
In analyzing the chords themselves, the locations of resistance to chord translation (braced frames etc) do matter. They'll affect:
- the peak force in the chord.
- the distribution of force in the chord.
- the manner in which the chord's axial deformation will add a flexural component of deformation to the diaphragm's shear deformation.
As for the four sided diaphragm case: sure, we could treat that as a pair of cantilevered diaphragms. Similarly, we could treat a simple span wide flange beam as a pair of cantilevers that are fixed to one another at mid-span and "cantilevering" from that mid span connection. And whether we go with a simple span diaphragm or a pair of faux cantilevered diaphragms, there will be "chords". Just differently loaded chords. I think that we typically go with with the simple span assumption on four sided diaphragms because:
- It's simple.
- For the most part, we expect it to be a better representation of true behavior.
- For the shear component of diaphragm deformation, it actually makes no difference.
- It does not require the presence of lateral resisting element along the chords which is expedient.
In my experience, it is true that the presence of lateral load resisting elements along chords alters their behavior and loading in ways typically not accounted for by designers. That's often conservative but not always. I, myself, do it no differently and no better than anyone else. I just think about it pretty hard.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.