This depends on the person you ask, especially with different beliefs. You can ask a scientist and he’ll explain the theory of gravity. You can ask a flat-earther and they’ll explain that the sun somehow affects certain parts of the planet at a time and other questionable theories. You can ask a religious person and they’ll likely say what the scientist says, but that it is in god’s will that it be so. Repeat this for most religions unless they have specifically defined it or aren’t monotheistic.
Buddhism does somewhat mention it in its more esoteric tantras, I imagine this is true for most religions, whether that be Islam, Christianity, Judaism, Hinduism, Taoism. etc. But likely both the moon and sun are mentioned somewhere or represent something within that religion. I imagine the asiatic religions as they seem to like to represent certain things or even gods using certain imagery or items, as large as the moon or as simple as chopsticks sticking out of a bowl of rice, as when attending a funeral in Japan, usually these are offered to the dead, as opposed to resting on the rim of the bowl. Doing the former in public is quite distressing.
I digress. In short, the sun and moon do “technically” fall visually from the horizon, but our language is complex and it can wax lyrical sometimes, conjuring up words to express that without making it sound slightly odd, trying to imagine a huge object such as the these “falling” seems ridiculous when thought about too much.