At about 600 B.C. Lehi leaves Jerusalem with his family. At some point after they arrive in the promised land, Nephi is commanded to make plates. See 1 Nephi 19:1. These are the ones we refer to as the Large Plates of Nephi. Later (30 years after Lehi left Jerusalem) he is commanded to make another set of plates. See 2 Nephi 5:30-31. These are the ones we refer to as the Small Plates of Nephi.
The large plates of Nephi are passed from one Nephite king to the next.
The small plates of Nephi are passed from Nephi to his brother, Jacob. Then to Jacob's son Enos, etc as we can read in the small books of Jarom and Omni. Amaleki is the last one to engrave on the small plates of Nephi. He has no descendants and the plates are full. See Omni 1:25, 30. So he gives the small plates to King Benjamin, who already has the large plates. From then on, the small and large plates don't have separate keepers anymore but are passed on together to the next record keeper: Mosiah - Alma I - Alma II - Helaman I, etc. But the small plates are full and the large plates is where they engrave the record now.
The large plates up until King Benjamin contain a lot of secular stuff, but also spiritual it seems. The small plates are more focused on spiritual things. When the small plates are full, the large plates are now used both for governmental affairs, wars, etc. but also sermons, prophecies, etc.
Fast forward to 320 A.D. The plates are handed to Mormon. He makes a new set of plates (the plates of Mormon) where he engraves an abridgment of the Large Plates of Nephi. When he is halfway through, he finds the Small Plates of Nephi. The fact that it takes him so long to realize they exist suggests there is a large amount of records, not just the plates of Nephi. Anyway, he likes what he sees and decides to include them, also because he feels prompted to do so. It seems to me that he just attaches or puts them together with his other plates where he is making an abridgement of the Large Plates of Nephi. But the Small plates of Nephi are left as is. He includes a comment about it in the Words of Mormon, see verses 3-7.
Fast forward to 1828. Joseph Smith dictates the translation of the Book of Mormon with Martin Harris primarily as scribe. He dictates the record which is Mormon's abridgement of the Large Plates of Nephi. When they get to King Benjamin, Martin Harris wants to show the written pages to his wife and relatives and loses them as we know. After several months, instead of doing that translation all over again, Joseph Smith continues to dictate from the rest of Mormon's abridgement of the Large Plates starting with what is now Mosiah Chapter 1 (at least so the evidence suggests). He dictates to the end of Moroni and then dictates 1st Nephi to Omni from the Small Plates of Nephi. They cover more or less the same time period as the part that Martin Harris lost. Oliver Cowdrey is the primary scribe in this period.
So the translated Book of Mormon we have today is obtained from
- The Small Plates of Nephi from 1st Nephi to Omni, unabridged
- The Plates of Mormon consisting of his inserted commentary between the small and large plates of Nephi (Words of Mormon), his abridgement of the Large Plates of Nephi from Benjamin up to his own time (Book of Mosiah - 4 Nephi) as well as his own words (Mormon 1-6) and the words of his son Moroni (Mormon 7-9 + Book of Moroni). Moroni also abridged the record of the Jaredites on those plates, which is the Book of Ether