Unsure if Math is the correct place to post this but I would like a geometric answer if possible.
When we say an item is upside down, does it mean that it is flipped vertically or that it is rotated 180 degrees? For example, a lower case $\lambda$ may be considered an upside down y as it seems like a flipped y, but it does not seem so if it is rotated 180 degrees.
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When I hang a painting upside-down, it is understood that I rotated it $180^\circ$ such that the front of the painting is still seen.
If you want to describe the situation where a change results in having the back of the painting seen, you would say "frontside-back." This could be either a flip along the vertical axis ("about-face") or a flip along the horizontal axis ("frontside-back and upside-down").
This is probably a better question for English Language. I think there is a big difference between two dimensions and three dimensions. If I am editing a graphic and ask that it be turned upside down I would expect a flip, not a rotation by $180^\circ$. If I have a solid object and turn it upside down I expect it to retain its handedness. It is clear the vertical axis is inverted but one (and only one) of the horizontal axes needs to be inverted as well. That means it is a $180^\circ$ rotation around one of the horizontal axes.