I used to be in regular email contact with William Rhodes, discussing his findings and the field of electrolysis and WFCs in general, and always found him to be a very decent, down-to-earth guy. It's been a few years since I've made contact with him, and to be honest I'm not sure he is even still with us as he was no spring chicken then.
Anyway, for anyone that has not seen it, here is a link to William Rhodes' paper detailing his findings related to common duct electrolyser gases. If you have never seen or read it, do so. It's extremely informative.
http://brownsgas.com/browns-gas-oxyhydrogen-hho-gas/browns-gas/william-rhodes.html
As far as Chris Eckman is concerned, long ago I read his paper: 'Plasma Orbital Expansion of the Electrons in Water', and did my own in-depth analysis of it.
I found quite a few blatant errors in his science that concerned me and was unable to see how he came to the conclusion that that the water molecule was somehow electrically expanded.
The most interesting and useful info came from his mass spectrometer findings which were accompanied by a detail graph.

The one peak on Eckman’s gas analysis graph that demands the greatest attention has to be the 5th highest peak that he labels as, ‘Plasma Expanded Water’. We know this lies somewhere between the atomic mass 18.042 of the second water vapour peak and the 22.992 atomic mass of the sodium peak, but for some reason he does not provide an exact figure. And as the x axis of the graph is clearly not linear, it may be that this substance still has an atomic mass of 18… something, and so would be a third water vapour peak, and due to excess electrons, be heavily negative in nature, ie an ion.
It seems quite apparent that the biggest difference between hydroxy gas from tanked or bottled hydrogen and oxygen when compared to that of a common-duct electrolyser gases, is the water vapour content.
Whereas you would expect there to be none (or very little) water vapour in bottled hydrogen and oxygen due to the drying process, water vapour is clearly abundant in the gas mixture evolving directly from a common-duct electrolyser.
As bubbles of hydrogen and oxygen erupt from the surface in an electrolyser, the hydrogen bonding of the water maintains a thin film of liquid water over the emerging gases and indeed it is the encompassing liquid water film that highlights the gases in the form of visible bubbles. As the evolving gases leave the surface of the water, the hydrogen bonds try to maintain their hold, but at some point the surface tension becomes too great and the bubble effectively pops. This action will cause some molecules of the liquid water to be thrown up where it can evaporate into gaseous form. Hence we get water vapour along with hydrogen and oxygen from our common-duct electrolysers.
Now, to my mind, this will happen with any common-duct electrolyser, be it straight dc or pulsed, and indeed any electrolyser whereby the resulting hydrogen and oxygen are not passed through a drier. So the question is: Is simple water vapour a major player in the properties of common-ducted electrolyser gases?
If you think about it, because of the abundance of water vapour, the one thing we that we can't readily get from our electrolysers unless we introduce gas driers, is just pure oxygen and hydrogen.
So, if we consider a stoichiometric mix of pure oxygen and hydrogen to be what is known as Hydroxy or Oxyhydrogen, then what we produce in even standard DC common duct electrolysers is not the same because at the very least it contains a lot of water vapour.
Throw in pulsing electrolysis, with the possibility of creating plasma electrolysis conditions or indeed cavitation, and we have yet another different gas mixture.
So as I see it, we have at least 3 distinctive gas mixture variants that are all very different, but generally (and simply depending on personal preference) given one of these all-encompassing names, Hydroxy, Oxyhydrogen, Brown's gas, Rhodes' gas, Ohmasa gas, HHO, etc. with nothing to distinguish one from the other.