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I think you can remove some confusion by removing the term "rope," cordage with no job, and inserting " line," as in a rope with a job...
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I do not believe that anyone will be " enlightened " as to what type of system is being used and how it may differ from others, by redefining a component, the rope, they all share.
There is very little confusion among climbers when using the current terms of SRT or SRWP. A brief explanation of the words behind the acronyms is all that is required for clarity.
Unfortunately, the word "single" as commonly used in SRT brings with it some negative and inaccurate perceptions when also used in SRWP, not by the climbers, but by people in the periphery, such as regulators and a handful of old, gray-beard trainers. The perception is that "single" is somehow inferior and less safe than "double". There is also the history of the SRT ascent/descent only systems and their severe limitations and safety requirements. Without a separation of terms and understanding these things tend to get lumped together.
As users we all know that we have been climbing on one rope regardless of the system, DdRT or SRT. What has changed are the tools involved allowing an anchored/stationary rope to be used in an all-encompassing, 3-directional manner (safe movement in all directions) without a change over.
I think we could leave the often used and well understood SRT as "Single Rope Technique". However, with the new tools and their abilities, it might be more accurate with less potential confusion and negative perceptions to refer and explain SRWP as a "Stationary Rope Work Positioning"?