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 Summary 

 Rabbi Yochanan: The shehechyanu blessing is recited on the last day of Sukkos [Shemini Atzeres, because it’s considered a new Yom Tov] but not on the last day of Pesach.

 Rabbi Levi bar Chama some say Rabbi Chama bar Chanina: You can know that this is so because Shemini Atzeres is different from the rest of Sukkos in three ways: Sukkah, Lulav and Nisuch Hamayim. These mitzvos are not done on Shemini Atzeres.

And according to Rabbi Yehuda that a lug was poured on all days (according to the Tanna Kamma 3 lug were poured on the first seven days only) including Shemini Atzeres, it is different in two ways. 

 Challenge: If so, a shehechyanu should be recited on Shvi’i Shel Pesach too, since it is different in the matter of Matzah, as we learned “On the first night there is an obligation to eat matzah even if one is not hungry, for the rest of Yom Tov there’s no obligation”.

 Resolution: What’s the comparison? Shvi’i Shel Pesach is only different from the beginning of Yom Tov at night but its day is not different from the preceding days. Shemini Atzeres is different from all days of Sukkos. (The following Amoraim are not arguing, they’re all adding). 

 Ravina: Shemini Atzeres is different from the day before, Shvi’i Shel Pesach is only different from the beginning of Yom Tov.

 Rav Papa: On Shemini Atzeres only a single Par is brought as opposed to the prior days where multiple Parim are brought.

 Rav Nachman bar Yitzchok: With regard to Shemini Atzeres the possuk begins “On the eighth day”, but with regard to all other days the possuk begins “ And on the ___ day”

 Rav Ashi: With regard to Shemini Atzeres the possuk says “According to its procedure”, but with regard to the seventh day the possuk says “According to their procedure”, to sum up all the prior days.