Both are correct. Use "autumn" for formal or poetic writing, and "fall" for everyday conversation (especially in North America).
Astronomically, autumn begins with the autumnal equinox, usually occurring around September 22nd or 23rd in the Northern Hemisphere. During the equinox, the Sun crosses the celestial equator, resulting in nearly equal durations of day and night across the planet. Following this point, the Earth's tilt—specifically 23.5 degrees relative to its orbital plane—causes the Northern Hemisphere to tilt progressively away from the Sun. This reduction in solar insolation is the primary driver of the season's cooling temperatures. what is fall season