At the sight of the nymph Urvashi the seed of Mitra and Varuna falls into a water jar; Agastya rises from the jar and Vasishtha is found on a lotus. Later texts add the quarrel with Nimi as the reason Vasishtha needed a new birth.
The Vasishtha family hymn tells its founder that he is the son of Mitra and Varuna, born of their love for Urvashi, a drop that the gods laid on a lotus, sprung from the Apsaras; both gods bedewed the pitcher and Mana rose from its midst. The Brihaddevata orders this: the seed fell in an overnight water jar at a sacrificial session, Agastya arose peg-sized from the jar, and Vasishtha was found on a lotus held up by the All-gods when the water was drawn.
Bodiless after Nimi's curse, Vasishtha asks Brahma for a body and is told to enter the seed of Mitra and Varuna. Mitra is ruling Varuna's realm when Urvashi arrives. Varuna desires her; she says Mitra asked first, and Varuna places his seed in a vessel. Mitra curses her to live with Pururavas. From the vessel, which also held Mitra's seed, Agastya is born first and tells Mitra he is not his son; Vasishtha follows and becomes priest of the Ikshvakus. Nimi chooses to live in the eyes of all beings.
What is different here:
Adds a cause (Nimi's curse), Brahma's instruction, rivalry between the two gods, Mitra's curse on Urvashi, and Agastya's disowning of Mitra. No lotus and no All-gods.
Nimi, son of Ikshvaku, begins a thousand-year sacrifice with Gautama because Vasishtha is engaged by Indra. Vasishtha curses the sleeping king to lose his body and is cursed in return. His spirit joins those of Mitra and Varuna until, through their passion for Urvashi, he is born again. Nimi is set in the eyelids of all creatures; Janaka is produced from his body.
What is different here:
Tells the quarrel fully and the rebirth in one sentence; no jar and no Agastya.
In a list of the Adityas' families: on seeing Urvashi both Mitra and Varuna shed seed, which was kept in an earthen pot; Agastya and Vasishtha appeared from it and are the common sons of both. Mitra's wife is Revati and their sons Utsarga, Arishta and Pippala.
What is different here:
Genealogy only; names Mitra's wife and other sons.
Sources: Hymns of the Rigveda, tr. R. T. H. Griffith (1896), hymns read for the Vedic layer; The Brhad-devata attributed to Saunaka, ed. and tr. A. A. Macdonell (Harvard Oriental Series 6); The Ramayana of Valmiki, tr. Hari Prasad Shastri (1952-59), Uttara Kanda; The Vishnu Purana, tr. H. H. Wilson (1840); Srimad-Bhagavatam (Bhaktivedanta Vedabase)