I agree with the Triple 2 step. 2 sets of chasse, then a walk walk, the triples replace the Slow Slow of the CW Two Step.
The other you are referring to as the Rhythm two step, is the way the old times use to dance the Two Step. Leading with the left, triple, then leading foot right triple step. That was all that was to it. Find a person older than 60 and ask them to two step (if they haven't been to any dances lately or classes) and I betcha they will triple triple. There are still some areas where that is the only way the do it. So Folk dance is a good label. Delighted