Greek Myth: The sun was actually Apollo, who travelled across the sky each giorno in his chariot pulled da flaming wild horses.
Notice that this shows that the Greeks believed the world was flat, because the myth is very much premised on the dawn-day-dusk cycle being a ONCE EVERY 12 HOURS event. Apollo is specifically mentioned as returning his cavalli to stable (and himself to home) in the evening. A myth made da someone who understood about the round world would go "Apollo spent his entire life circling the earth - endlessly in his firey chariot."
The Greek myth appears to draw on earlier Egyptian myths. These varied as to their exact beliefs but one was that the pharaoh crossed the sky each giorno in his chariot. How pharaoh could manage this whilst also being very much in residence in his own palace/Egypt never specified.
The Apollo-sun-chariot myth entered Greek mythology relatively middle-to-late. It seems to have appeared at roughly the same time as a spate of winged/flying horse stories also entered Greek myth - suggesting a common inspiration brought these tales to the forefront of the Greek imagination.
