There are a number of differences between the Mars of our world and the Barsoom of John Carter that cause us to ask the question, "Are the two worlds the same?" When the Viking I and II landers first alighted upon the surface of Mars, they only found dust and rock, not an ochre plain. No ancient cities, no incubators. The Mars we know is too inhospitable to support any life other than the simplest of microbes; human life is impossible. The answer is no, Barsoom is not Mars.
One major difference between the worlds is the moons. The moons of Mars, Phobos and Deimos, orbit in a fairly normal plane, perpendicular to the planet's axis of rotation. Both are small, airless rocks, almost too dark to be seen with the naked eye. Their proximity to the planet means they cannot be seen from the northern or southern polar regions. By contrast, the moons of Barsoom, Cluros and Thuria, appear to hurtle through the heavens in a most unnatural polar orbit. John Carter describes both as being clearly visible from the Otz Mountains in the land of the Holy Therns (GoM, 6).
It appears also that John Carter's adoptive homeworld is quite a flat place, for "Upon the entire surface of that ancient planet I never before had seen a hill or mountain that exceeded four thousand feet in height above the dead sea bottoms..." (GoM, 2). Had Burroughs known about the great Mount Olympus of the real Mars, it is unlikely that he would not have included it in his chronicles. A volcano towering 25,000 meters above the surrounding plains presents far too many adventuring opportunities for an imaginative writer to simply ignore. John Carter's description of Mars is thus probably due to limited scope of travelling.
Perhaps Barsoom is Mars, but not the Mars that we know. When John Carter and Ulysses Paxton traveled to the red planet they both left their physical bodies behind on Earth. How, then, did they manage to have a physical existence on the planet of their arrival? If the two worlds are the same, how do Carter and Paxton manage to have a physical existence on to planets in the same solar system?
When we look at Mars through our telescopes and satellites, we do not see Barsoom, and yet the Barsoomians are able to see Earth's tiniest details with theirs. The more we look, the less Mars appears to be Barsoom.
It may be that Barsoom resides in another dimension, a uniquely Barsoomian dimension. When Carter and Paxton travelled to Barsoom, they not only left Earth, they left Earth's dimension, travelling through the higher reaches of space-time to appear naked and unarmed in the dimension of Barsoom.
To our knowledge, only two Earthmen have been able to traverse the void of space-time to the world of Barsoom. However, that does not appear to rule out the possibility of others completing the journey. Perhaps Carter and Paxton really did die, and Barsoom is a kind of Valhalla - a warrior's paradise of eternal life and adventure.
Fortunately, this only serves to make Barsoom so much more interesting as a roleplaying world. In the "Maps" section, my first attempts at mapping Barsoom begin by juxtaposing the two dimensions and asking "what if Barsoom really is Mars?" The juxtaposition creates a third unique world, a Mars quite alive and inhabited, and a Barsoom slightly altered to fit its counterpart.