[Terquem]

I have not witnessed it myself, but I've been told the stars look different in the southern hemisphere than they do in the northern hemisphere.

I can only imagine that a sailor, who navigates by the same stars above her head for her entire life, who suddenly, in the blink of an eye, is below a set of stars unfamiliar to her would either first, accept that they have moved to another part of the world where the stars above are not the same, or second, moved to another world. Since measurements of longitude are practically impossible if time is not accurate while moving across distances, and latitude is generally derived from the position of the sun above the horizon in the sky relative to north or south, and with all these things changing instantaneously, north south, east west, regardless of time. The stars above would be no real help to someone who moved from New Hampshire to Perth with no way of ever going back.

Without sophisticated technology or advanced magic, it would be difficult to prove one theory over the other, wouldn't it?

and without rapid forms of physical travel, actually knowing the difference is useless. Sailing around any, "Earth" sized planet, under sail, should take years, accidentally moving to another world while at sea could be something the sailors would only realized happened if a different sun or moon rose in the sky, or the stars appeared different, but for the traveler, the water beneath the ship doesn't change, and to them it feels like they have only moved to another "place" on a very large "world"