In North India, Diwali commemorates the return of Lord Ram along with Sita and Lakshman from his 14 years of exile after killing Ravana.
In Tamil Nadu and generally in South India, Deepavali is celebrated to commemorate the killing of the demon Narakasura by Lord Krishna. In Karnataka, it is observed as Bali Paadyami to mark the day of King Bali's return to his subject once a year. In Kerala, Deepavali is a low-key affair and some people consider it as the return of Lord Ram from exile.
There may be difference in date and myth but the central theme that good wins over evil, remains the same.
