people who deal with and use soundex frequently will refer to that particular flavour of soundex as Russell or NARA soundex.
Perhaps. Google (surprisingly) only knows of 550 books containing the word Soundex. Five say "NARA Soundex" and just under half say "Russell Soundex." In my thirty(?) years as an amateur genealogist, I had never noticed anyone using either term no using Soundex for other algorithms, though I do see examples now when I hunt for them.
Interestingly, I found the term Soundex in the 1913 Boston University Bulletin in a course description. Since Russell's first patent was in 1911, I suspect the Uni. was referring to a different algorithm.