What are the differences between Shabbos and Yuntiv?? On both days we get dressed up, don't go to work, go to shul for a longer davening than normal and most importantly – eat a LOT. But what are the DIFFERENCES??
One is that Shabbos does not at all depend on human beings. Hashem made Shabbos the seventh day of the week for once and for all and that is it. But Yuntiv was determined by the Beis Din based on when witnesses came to testify about the new moon. Shabbos is purely Hashem's creation so we must be completely passive and do no melacha. Yuntiv symbolizes our human input which would explain why we are allowed to cook on Yuntiv.
Another distinction was taught by the Meshech Chochma: Shabbos is a time where the emphasis is on the individual – therefore one is not allowed to carry outside - אל יצא איש ממקומו. On Shabbos one is supposed to sit and learn Torah alone. We connect to other Jews by virtue of the fact that we are all serving Hashem. So there is achdus between Jews but in a less obvious way.
In contrast, Yuntiv is a time for everyone to get together. The word for Yuntiv מועד means to get together. להתוועד. In Yiddish – to farbreng. We are allowed to carry outside even without an eruv, and we are allowed to cook for guests that come. This way we can connect to others. We are all supposed to go up on Yuntiv to Yerushalyim to the Beis Hamikdash to be with all of Klal Yisrael.