Before us is Mishnah 6 in chapter 6 of Maseches Nazir, which deals with the order of purification and the bringing of offerings by a nazir who became tamei, and with the comparison between his law and that of a metzora. A nazir who became tamei and wishes to purify himself is required to shave all the hair of his head and to bring offerings, and the Mishnah comes to spell out the order of the stages: "Keitzad?" - How so?
The order of purification of a nazir who became tamei:
He is sprinkled with the waters of the red heifer on the third day of his tumah and on the seventh day - this is the ordinary process of purification that applies to anyone who became tamei through contact with a corpse.
Afterward he shaves his head on the seventh day.
And on the next day, the eighth day, he brings the offerings of a nazir tamei.
He shaved on the eighth day - the view of Rabbi Akiva:
If he delayed the shaving by one day and did not shave on the seventh day but on the eighth, Rabbi Akiva holds that he brings his offerings that very day, on the eighth day itself. The reason: a nazir tamei brings his offerings on the day after his purification, and his purification was already completed on the seventh day - not on the day after his shaving. Therefore, even though he shaved on that very day, he brings his offerings on that same eighth day.
Rabbi Tarfon's question - what is the difference between this and a metzora?
Rabbi Tarfon said to him: what is the difference between this law and the law of a metzora? A metzora too, who has been healed and comes to purify himself, must shave - admittedly his entire body and not only his head - and he shaves on the seventh day and brings his offerings on the eighth day. And the halachah there is that if he shaved one day later, on the eighth day, he does not bring his offerings that same day but on the following day, the ninth day. Why, then, does the nazir bring his offerings on the day he shaves, while the metzora brings his only on the day after his shaving?
Rabbi Akiva's answer:
The nazir - his purification depends on his days: Once the days have passed over him, the waters were sprinkled on him on the third and on the seventh, and he immersed in a mikvah on the seventh day - he is tahor. Once he has become tahor, even though he has not yet shaved, and even if he pushed off his shaving to the next day, he brings his offerings on the eighth day, which is the day after his purification.
The metzora - "taharaso teluyah b'tigelachto" - his purification depends on his shaving: With the metzora, purification is not accomplished through the sprinkling of the chatas waters, for that sprinkling is unique to the tumah of a corpse and not to the tumah of a metzora. His purification depends on his shaving, and he immerses in a mikvah only after he has shaved. Therefore, if he was ready to be tahor on the seventh day but did not shave until the eighth day, he must immerse and become tahor after the shaving of the eighth day - so it turns out that he is not truly tahor until after his shaving, since his immersion comes later than it.
And he may not bring an offering unless sunset has passed over him:
The nazir immerses in a mikvah independently of his shaving, and his immersion is on the seventh day - therefore sunset passed over him at the end of the seventh day, and the shaving does not prevent him from bringing his offerings on the eighth day. But the metzora, who immerses only after his shaving - and suppose he shaved on the eighth day - it turns out that his purification was completed on a day that has already passed, and he cannot bring his offerings until sunset passes over him, the night following his immersion. His offerings are therefore pushed off to the ninth day, unlike the nazir, who is not pushed off.
In summary: a nazir who became tamei is sprinkled on the third and on the seventh, shaves on the seventh and brings his offerings on the eighth; and if he shaved on the eighth - according to Rabbi Akiva he brings his offerings that same day, since his purification depends on his days and not on his shaving, and sunset has already passed over him. The metzora, however, whose purification depends on his shaving and who immerses only afterward, if he shaved on the eighth, his offerings are pushed off to the ninth day, after sunset has passed over him.