Of course the two kingdoms were originally one in Elendil's time. And perhaps
the concept of "Rangers" as a light mobile scouting force does go back to the
time of Elendil's armies of the Dunedain at the end of the Second Age. That's a
very broad, generic concept for a fighting force, like saying Elendil had
"cavalry" so all cavalry units of Gondor and Arnor that were ever armed and
organized have a common origin. I don't think that possibly valid speculation
really answers this question.
My answer to Temujin, and to your speculative answer, related to the "Rangers
of Eriador", or whatever you want to call the Men who followed Aragorn in
guarding the Westlands in the last millennium of the Third Age; and to the
"Rangers of Ithilien", a guerilla scouting force established in Ithilien after
the Enemy took over that fief of Gondor.
I don't see any reason to say they were aware of each other, or that they had a
"common origin" in the meaningful sense of their own organizational
history.
