In the previous Mishnah we learned that at this point, at the conclusion of Maggid, we begin to recite Hallel. Now the Mishnah asks: "Ad heichan hu omer" - up to which point in Hallel do we recite here? For we do not say the entire Hallel at this point; the rest of Hallel is said after Birkas HaMazon.
How far do we recite Hallel:
"Beis Shammai omrim: ad 'Em habanim semeichah'" - only until the end of the first paragraph, and no further. The reason is the concern that if we go on at length, the children will fall asleep.
"U'Veis Hillel omrim: ad 'Chalamish l'mayno mayim'" - we continue for one more paragraph, because up to that point the Exodus from Egypt has not been mentioned at all; it is mentioned only in the second paragraph.
"V'chosem bi'geulah":
After Hallel we conclude with the berachah of redemption, and the Mishnah brings a dispute regarding the wording of the berachah and its closing.
"Rabbi Tarfon omer" - the wording of the berachah is "asher ge'alanu v'ga'al es avoseinu miMitzrayim", "v'lo hayah chosem" - and one does not conclude with the closing "Baruch atah Hashem, ga'al Yisrael." It is enough to say: "Baruch atah Hashem Elokeinu Melech ha'olam asher ge'alanu v'ga'al es avoseinu miMitzrayim."
"Rabbi Akiva omer" - we add further to this, and because of that addition we also close with a berachah: "Ken Hashem Elokeinu v'Elokei avoseinu yagi'einu l'mo'adim v'lirgalim acheirim haba'im likraseinu l'shalom" - that we should merit to reach the coming festivals and holidays in peace; "semeichim b'vinyan irecha v'sasim ba'avodasecha"; "v'nochal sham min hazevachim u'min hapesachim" - from the offerings, from the chagigah offering and from the pesach offering, and so on as the wording appears in our Haggadah, until the closing "Baruch atah Hashem, ga'al Yisrael".
Rabbi Akiva's reasoning for requiring a closing: when additional passages are added to a berachah, it must be concluded with a closing of "Baruch atah Hashem."
In summary: in this Mishnah we examined the question of how much of Hallel is recited at the conclusion of Maggid - Beis Shammai say until "Em habanim semeichah," and Beis Hillel say until "Chalamish l'mayno mayim," because only in the second paragraph is the Exodus from Egypt mentioned. We also learned the dispute between Rabbi Tarfon and Rabbi Akiva regarding the wording of the berachah of redemption: according to Rabbi Tarfon it is enough to say "asher ge'alanu v'ga'al es avoseinu miMitzrayim" without a closing, while according to Rabbi Akiva we add the request concerning the festivals and holidays and eating of the zevachim and pesachim, and therefore we close with "Baruch atah Hashem, ga'al Yisrael."