The Moon appears flipped upside down in the southern hemisphere vs the northern.
In cosmological terms (cosMOlogy is the study of the universe, cosMETOlogy is makeup and cosmetics) there is no predefined up and down, but more humans live in the northern hemisphere than the south. As such a lot of popsci refers to north as up and south as down, and this is the convention for immobile maps. Those of the big pieces of paper kind usually use put north up, whereas computer maps often have north rotating around as the mobile device moves. Google Maps lets you lock north to up, but will free spin otherwise.
This up-down ambivalence is not found everywhere. For example a boat has a definite top and bottom, and getting the two confused will make the thing sink. Tree branches grow up, roots grow down, and there isn’t a lot of confusion between the two. People have their heads on top and feet on bottom, usually. These are what we call preferred reference frames. One can, via math, make any reference frame up or down, but some are much more work than others. By convention, down is the direction the gravity force vector points, and up is the other direction.
Cosmology doesn’t have such preferences, so up is whichever way we pick. The more pedantic among us will eschew terms like up and down to refer to directions unencumbered by gravity.
North of the Equator our heads generally point more north than south. Up and north do have some overlaps. South of the Equator our heads generally point south. Up and south have some vector overlap.
The Moon is the same Moon in both north and south, so the part of it we think of as the top, the bit that is furthest ‘up’ in our personal reference frame, depends on where we stand. At the North Pole this bit, the uppermost part of the Moon, will be the northernmost part of the Moon. At the South Pole the uppermost bit is the southernmost part of the Moon. Inbetween ‘up’ will point to an edge, and where that direction points depends on our latitude on Earth.
All of that is a long bit of saying that in Chile the Moon will look upside down compared to the Moon in Alaska. You can see this by following Moon pictures on Instagram. Look for some southern city’s hashtag and #moon, and compare the moon to how it looks in the north.
This would not happen on a flat Earth. If you really don’t trust Insta, and if you don’t I understand, a plane ticket to Chile is about a thousand bucks. You can prove it to yourself and have a great vacation. You might need a lens for your camera or phone depending on resolution and focus, but a decent one is less than a hundred bucks and will give decent lunar resolution.