The parshiyot we read during these weeks discuss Shabbat. Every Shabbat, we say kiddush to sanctify Hashem’s name (Pesachim 26a) and to differentiate between Shabbat and all other days. We still make Kiddush in shuls despite the fact that most people make Kiddush again at home in order to be mekadesh Shem Hashem in public. We also say havdalah at the conclusion of Shabbat. There are many halachic issues regarding havdalah that need to be discussed.
There is a machloket whether havdalah is a mitzvah d’orayta or d’rabanan. The Minchat Chinuch (Mitzvah 31) says that kiddush is also a mitzvah d’orayta and he says that just like kiddush is d’orayta, havdalah is d’orayta. This is derived from the pasuk (Shemot 20:8) “Remember the Shabbat to sanctify it;” sanctify Shabbat at its entrance with kiddush and at its departure with havdalah. However, the Rosh (11:3) and Pri Migadim (Orach Chayim 296) hold that havdalah is only a mitzvah d’rabanan. Chazal decreed that the tzibur should say “ata chonantanu” in the beracha of “ata chonein” on motzei Shabbat in order to standardize havdalah (Berachot 33a and Shulchan Aruch Orach Chayim, 294:1). However, one still has to recite havdalah al hakos. Poskim argue about which recitation is the main fulfillment of the Torah obligation and which is secondary. The Mishna Berura (296:1) considers havdalah in the shmoneh esreih as the primary one. However, the Chatam Sofer (Orach Chayim, 21) understands that the primary recitation is the havdalah al hakos. The Rambam (Shabbat 29:5), explains that it is assur for a person to eat, drink, or do melacha before havdalah.
The Brisker Rav infers from the Rambam’s formulation, which seems to not differentiate between the issur melacha and issur achila, that these issurim sprout from the obligation to perform havdalah and have nothing to do with the issur melacha of Shabbat. In Shabbat (150) the Mishnah explains that a person can watch his peirot as the day gets dark if it is close to his techum Shabbat. The Gemara applies this even if one didn’t do havdalah yet. The Gemara asks - how can one fulfill his needs before doing havdalah? The Gemara gives two answers in its conclusion. One answer is that indeed, the permission to watch one’s peirot only applied if one already made havdalah al hakos. Another answer was that he made a heker by saying “hamavdil ben kodesh l’chol”. Many Rishonim argue regarding this if one needs havdalah with shem and malchus al hakos or if it is sufficient with just this heker. The Rif implies that this hekeir sufficed bedieved for melacha, achila, and shtiah, while the Ran writes that it suffices lechatchila for melachah but doesn’t suffice even bedieved for achila. The Brisker Rav explains this based on his fundamental understanding of the Rambam. According to the Rif, the three things forbidden before havdalah are all based on the chovat havdalah associated with them, the source of this issur. Hence, bedieved, one can fulfill his obligation vis-à-vis all three with just this hekeir. According to the other opinions, the issur melacha sprouts off of dinei Shabbat, which is a separate mitzvah from havdalah altogether, allowing for this hekeir to be enough to matir the issur melacha.
The Brisker Rav adds that according to the Rambam and Rif, since the issur melacha is not an extension of Shabbat’s issur melacha, it may prohibit activities that are normally permitted on Shabbat and it may permit activities normally prohibited on Shabbat. This is why the Shulchan Aruch (298) ruled that one may light fire and carry in a reshut harabim before havdalah. This would not be true according to the Ran who holds that the issur melacha before havdalah is an extension of the regular issur melacha on Shabbat.