The story
The day belongs to Yama, the lord of death, and his sister Yamunā, the river. She invited him to her home and fed him, and he was so pleased that he granted that any brother who eats at his sister's table today, and receives her mark on his forehead, will not fear death. The older name of the day is Yama Dvitīyā for this reason.
A second telling gives the day to Kṛṣṇa, who visited his sister Subhadrā after killing Narakāsura and was welcomed with a lamp, a garland and a tilak.
Where Rakṣā Bandhan has the brother pledge protection, Bhāī Dūj has him come to the sister's house as her guest: the direction of the visit is the point.
