Priesthood is a complex subject in Mormonism. The very meaning of the word has ebbed and flowed. Below, I focus on ecclesiastical office in a narrow sense. I only consider church structures involving the practice of ordination, not “setting apart” in the modern vernacular.
. . . we lay our hands upon your head and confer upon you the Aaronic Priesthood and ordain you a deacon in The Church of Jesus Christ of Latter-day Saints.
. . . we lay our hands upon your head and confer upon you the Melchizedek Priesthood and ordain you an elder in The Church of Jesus Christ of Latter-day Saints.
The language “confer upon you . . .” is the point of this post.
The words seem natural given that Mormons see their priesthood as having the taxonomic structure illustrated in the two diagrams.
It is a fact that Joseph Smith’s revelation in the spring of 1835 (now available as verses 1-57 of Doctrine and Covenants 107) more or less outlines this grouping of priesthood offices. Prior to that revelation, offices were grouped in other ways and following the 1835 revelation, church speech and practice only gradually adjusted. The notions of Melchizedek Priesthood and Aaronic Priesthood as they appear in section 107 were back-written into some earlier revelations in the 1835 first edition of the Doctrine and Covenants.
But whatever changes the 1835 revelation wrought on Mormon thinking about priesthood I think it is important to state that the revelation helped cement 1835 Mormon views of priesthood and it is vital that we exercise some caution in trying to see that 1835 architecture in our readings of other scripture, ancient or modern, no matter how redacted. The 1835 revelation gives us a way to talk about Mormon priesthood, but not necessarily (in spite of the naming reasons offered in Doctrine and Covenants 107 — an issue I plan to discuss sometime) a ruling definition for other passages of scripture or Mormon literature, especially that of the nineteenth century. I think Joseph Smith might agree here: he saw the restoration as not just a return of the former glories, but a new way of looking at the old, the sometime sacralization of the secular and the expansion of religion aided by new revelation and inspired extension of definition.
Turning back to the point of this, the basic issues are folded into these two assertions:
(1) Joseph Smith, and for that matter Latter-day Saints up to 1900, saw the 1835 categories as a way to think about priesthood and jurisdiction. They did not see it as a liturgical warrant. When priesthood ordinations took place, there was no conferral of genus, only species. No one had the Aaronic/Melchizedek Priesthood “conferred,” just as no one had the “order of Jesus” conferred.
(2) After 1900, church President Joseph F. Smith began, on occasion, to advocate a conferral rite. When, after his death, the book Gospel Doctrine: Sermons and Writings of President Joseph F. Smith was published, it contained this advocacy as supported by his exegesis of Doctrine and Covenants 107.
As a result of President Smith’s view, his son, Elder Joseph Fielding Smith, and perhaps others, took up the idea. Elder Smith’s son-in-law and general authority Bruce R. McConkie, included the idea of conferral as part of the rite of initial priesthood ordination in his 1958 Mormon Doctrine. In the meantime, church handbooks were either silent on the subject, or outlined the pre-Joseph F. Smith pattern. It was not until the 1960s that we find church practice officially changed in favor of the Joseph F. Smith rite. The way we read texts is influenced by and then influences in its turn, every aspect of our lives. Don’t eat too many croissants.
 When a Mormon male is ordained to priesthood office for the first time, the congregation is invited to sustain the conferral of priesthood category as well as the particular priesthood office.
 Reference to priesthood office and position were in flux from 1830. Earlier revelations captured snapshots of that evolving referential structure.
 The language Joseph Smith used to describe John the Baptist’s appearance and actions was important in later evolution. But care is necessary in interpreting Joseph’s meaning in his 1838 recital of the event. Indeed, the whole angelic priesthood delivery mythos is in need of careful reanalysis. I’m not doing that here.
 This was seen as somewhat shocking by readers (it is important to understand the circulation of even general conference addresses was relatively small and so Pres. Smith’s ideas had small audience originally, and the way these speeches were seen . . . that’s another story). The result was a nearly immediate 2nd edition of the book with a letter from the new Heber J. Grant First Presidency, outlining that this was Pres. Smith’s opinion and that the historical modes of ordination without conferral were acceptable, correct and need not be altered.