Just as there is a mitzva to make havdala at the end of Shabbat, so too there is a mitzva to do so at the end of Yom Tov, giving verbal expression to the difference between the sanctity of Yom Tov and weekdays. Even when passing from Yom Tov to Hol Ḥa-mo’ed, there is a mitzva to make havdala. The laws pertaining to havdala are similar in some ways to those pertaining to kiddush. Just as one must mention the sanctity of Yom Tov both during prayer and over a cup of wine, so too, at the conclusion of the Yom Tov, one must recite havdala both in prayer and over a cup of wine. During Ma’ariv, the paragraph of Ata Ḥonantanu is inserted into the fourth berakha of the Amida.
The Sages ordained that melakha not be performed before the recitation of Ata Ḥonantanu, and that food not be eaten until after the recitation of havdala over wine. If one forgets to add Ata Ḥonantanu, he fulfills his havdala obligation when he recites havdala over wine, after which he may do melakha and eat. Similarly, women who do not generally pray Ma’ariv fulfill their havdala obligation with the havdala recited over the cup of wine. A woman wishing to do melakha before havdala should recite the phrase “barukh ha-mavdil bein kodesh le-ḥol” (“Blessed is the One Who distinguishes between the sacred and the mundane”). In this way she gives verbal expression to havdala and is permitted to do melakha. This also applies to a man who misses Ma’ariv and wants to do melakha before praying, as well as one who forgot to add Ata Ḥonantanu in the Amida and wants to do melakha before making havdala over wine.
There are two differences between havdala of Shabbat and havdala of Yom Tov: 1) After Shabbat, we smell a fragrance (besamim). This is because when Shabbat ends, the neshama yeteira (lit. “expanded soul”) departs and our spirit is despondent. In order to revive it, we smell a fragrance. However, on Yom Tov we are not granted a neshama yeteira, and therefore, it is not necessary to revive our spirit by smelling fragrance. 2) Only on Saturday night is there a mitzva to recite a berakha over a flame, because fire was created on Saturday night (SA 491:1; MB ad loc. 2-3). Thus, havdala after Yom Tov has only two berakhot: Ha-gafen over the wine and Ha-mavdil bein kodesh le-ḥol.
After Shabbat, every custom prefaces the berakhot of havdala with verses of blessing, because it is an auspicious time for drawing down blessing for the six weekdays. However, the night after Yom Tov lacks this special quality. The Ashkenazic custom, therefore, is not to recite these verses after Yom Tov, while the Sephardic custom is to recite them.