In the Land of Israel, the holiday of Sukkot is seven days long and the “eighth day” of the holiday is Shemini Atzeret, which is a separate holiday, as indicated by the fact that it does not have the mitzvot of lulav, of sukka or of the water libation. The situation outside of Israel is more complicated, since during the time of the Mishna when the announcement of the new month was made by the Beit Din HaGadol in Jerusalem, it was sent by messenger. Therefore, places outside of Israel could not be sure when the holiday actually began, and because of this uncertainty, they kept two days of Yom Tov. Diaspora communities continue keeping this tradition to this day, even though we now operate with a set calendar and all communities know when the new month and the holidays fall out based on the calendar.
Based on this, the “eighth day of Sukkot” presents something of a problem. Should we treat it as a separate holiday or is it still considered part of Sukkot?
According to the first version, all agree that Diaspora Jews are obligated to sit in the sukka on the eighth day; the disagreement is whether they make a blessing on the mitzva of sukka. According to the second version, everyone agrees that a blessing is not made on the sukka; the disagreement is whether people should be sitting in the sukka on that day at all.
The Sefat Emet explains that all opinions in the first version assume that there cannot be any problem with sitting in the sukka. Even the concern of bal tosif – that a person is not allowed to add to the mitzvot of the Torah – does not apply in this case, because no clear act of mitzva is being done in this case. Therefore you cannot lose anything by sitting there. This may help explain why none of the amora’im suggest that we should continue taking the lulav and etrog on the eighth day in the Diaspora. The Ran adds that as we have learned, taking the lulav and etrog after the first day of Sukkot is a Rabbinic obligation, and there is no reason to extend that Rabbinic obligation to a day that is, itself, considered Sukkot only from a Rabbinic perspective.
The rishonim grapple with the second version, however. Why should one of the amora’im rule that we not be obligated to sit in the sukka on a day that might be considered Sukkot? The Ran and the Ritva explain that this is only true because of the present day situation when we really do know the correct day of the holiday, and the people in the Diaspora keep two days of Yom Tov only out of respect for the traditions of their forefathers. Thus there is room to be lenient when the two holidays would end up in conflict with one-another.