TOSFOS in Shabbos (137b, DH Al) explains that the obligation to do Peri'ah is included in the Mitzvah of Milah, for we have a tradition that if the majority of the Atarah is covered with flesh or membrane (such that Peri'ah was not done), it is not considered a valid Milah. They are not different Mitzvos, but rather they are two parts to the single Mitzvah of Milah.

The Brisker Rav, as we quoted in the Insights, though, seems to learn that Peri'ah is completely separate from Milah. Indeed, Tosfos himself asks on his own view from the Mishnah there in Shabbos which clearly implies that Peri'ah is separate from the Mitzvah of Milah. Tosfos leaves this question unanswered.

However, the TOSFOS YOM TOV in Shabbos there (end of Perek 19) points out that Tosfos is following his own reasoning that he states in our Sugya (71b, DH b'Kuntrus). Tosfos learns like the Girsa of Rabeinu Chananel in our Sugya, that Avraham Avinu was also commanded to perform Peri'ah. According to the Girsa of Rashi (DH Im Ken), though, it is clear that Avraham Avinu's Milah did not include Peri'ah. Consequently, it is clear according to this that Milah and Peri'ah are two separate Mitzvos (as the TOSFOS CHADASHIM on the Mishnah in Shabbos writes). The Mitzvah of Peri'ah -- even though its source is only in the verses in Nevi'im -- is nevertheless a Halachah l'Moshe mi'Sinai. Yehoshua comprised a verse as an Asmachta for that Halachah l'Moshe mi'Sinai (as we find often). Accordingly, the wording of the Mishnah in Shabbos which implies that Peri'ah is a separate Mitzvah, is clear. It is according to this view that the Brisker Rav wrote his comments.

(Nevertheless, it is obvious that Peri'ah is not to be included as a separate Mitzvah in the count of the Mitzvos, since it is only a Halachah l'Moshe mi'Sinai.)

M. Kornfeld