Nephi never specifically named his plates with anything other than his name “plates of Nephi.” It is Jacob to whom we owe the name “small plates,” although for Jacob it appears to be a physical description much more than a comparative name. It is interesting to speculate how it is that Jacob knows that these plates are “small.” It can only be that there is another set of plates for comparison (and there were) and that Jacob had seen them (which is not surprising). What is only slightly surprising in this scenario, is that while Jacob was sufficiently familiar with the large plates to be able to use them as the standard of comparison he apparently knows little about these “small” plates. He would surely have known of their existence, and Nephi would have no reason to hide them, and in a small community most things are known. However, Jacob either does not know why they exist, or Nephi’s instructions are a formality rather than a necessary companion to the plates.
What appears most probable is that the large plates were the primary record, and as such were the public record, and Jacob would have had multiple occasions to see them (though he never gives any indication of having read them, as he certainly has the brass plates). The small plates would have been known to him, but perhaps only that they existed and they appear to be much more of a private text for Nephi.
Literary: Jacob‘s introduction to his own section on the plates is stylistically very different from Nephi’s introduction in 1 Nephi 1:1. That introduction was not only more formal, but it was formulaic. Nephi followed an Old World tradition of the colophon, a tradition with which he would have been familiar by reason of training and access to texts.
Jacob, on the other hand, is born in the wilderness. His early years are spent in the harsh environs of the desert crossing to Bountiful, and after that time spent in the new and challenging circumstances of the New World. It is obvious that Jacob’s instruction included the ability to read and write, but it is unlikely that he would have been exposed to the quantity of the written word as was Nephi. Even taking into account that Nephi may not have had as much an exposure as modern man, it is still certain that Jacob would have had less. The brass plates were with the Lehites, but it is unknown whether or not there were any other written records.
S. Kent Brown makes convincing case that Lehi kept a written record during the trek to the New World (Brown, S. Kent. “Recovering the Missing Record of Lehi.” In: From Jerusalem to Zarahemla. Religious Studies Center, BYU. 1998, pp. 28-54), but it seems unlikely that the extra bulk and weight of more books would have been a priority for the family. Thus Jacob learns to read and write from the materials at hand, and they do not include samples of texts with colophons, save Nephi’s alone.
Jacob seems to see his record as a continuation of Nephi’s record rather than his own work. Where Nephi’s introduction formally presented his name as author, Jacob gives his name almost as an afterthought.
Historical: The beginning of Jacob‘s record formally coincides with Nephi’s delivery of the small plates, 55 years after the departure from Jerusalem. Using Spackman’s date of 587 BC (Spackman, Randall. “Introduction to Book of Mormon Chronology.” FARMS reprint, 1993. P. 11, Spackman, Randall. “The Jewish/Nephite Lunar Calendar.” In: Journal of Book of Mormon Studies. 1998. 7:1:57) as the time of departure, Nephi gives Jacob the small plates in 532 BC. Following Sorenson‘s estimate of the ages of Lehi and Sariah’s sons, we have about a 20 year difference between the ages of Nephi and Jacob (Sorenson, John L. “The Composition of Lehi’s Family.” In: Nephite Culture and Society. New Sage Books, 1997, p. 21). Thus while Nephi was aged unto death, it was reasonable to give the plates to Jacob rather than to a son (though another reason for this will be proposed later) because Jacob could be expected to have a similar life expectancy to Nephi. Assuming Nephi was 16 at the time of the departure (again following Sorenson) he is about 71 at this point, and Jacob is now 51, with at least 30 of those years in the service of his people as their primary religious leader.