Aaronic Priesthood Conferred Twice?

[Gifted Fish]

I don't understand the series of events when John the Baptist visited Joseph and Oliver. John visits J&O and confers the Aaronic Priesthood on them. They baptize each other. Then they come out of the water and either confer (or ordain - depending on the account) the Aaronic Priesthood on each other again after John has apparently left the scene. (JSH 69-72)

Why did they need to get the priesthood twice? First I thought that maybe John just conferred the priesthood and then they ordained each other to a particular office, like we do today, but that doesn't really make any sense -- why couldn't John have just done both at the same time? Also, Joseph's history seems to imply that conferring and ordaining are basically the same thing (see verse 72).

[Gifted Fish]

Originally Posted by Adam

It is always a two step process: First, the priesthood is conferred. Second, the individual is ordained to an office. It is the same way today.

Joseph and Oliver are odd in that they were given the priesthood before they were baptized, but waited until after they were baptized to ordain each other to an office in the priesthood.

I don't think this is how Joseph wrote it - here's what JSH says:

68 We still continued the work of translation, when, in the ensuing month (May, 1829), we on a certain day went into the woods to pray and inquire of the Lord respecting baptism for the remission of sins, that we found mentioned in the translation of the plates. While we were thus employed, praying and calling upon the Lord, a messenger from heaven descended in a cloud of light, and having laid his hands upon us, he ordained us, saying:
69 Upon you my fellow servants, in the name of Messiah, I confer the Priesthood of Aaron, which holds the keys of the ministering of angels, and of the gospel of repentance, and of baptism by immersion for the remission of sins; and this shall never be taken again from the earth until the sons of dLevi do offer again an offering unto the Lord in righteousness.
70 .....
71 Accordingly we went and were baptized. I baptized him first, and afterwards he baptized me—after which I laid my hands upon his head and ordained him to the Aaronic Priesthood, and afterwards he laid his hands on me and ordained me to the same Priesthood—for so we were commanded.
72 The messenger who visited us on this occasion and conferred this Priesthood upon us, said that his name was John .... It was on the fifteenth day of May, 1829, that we were ordained under the hand of this messenger, and baptized.

There's no mention of offices or any gradations within the priesthood here. Maybe just a matter of semantics, but I just don't understand what actually happened.