There are two Ammons in the Book of Mormon. The one in this text was sent by King Mosiah three years into his reign (7:1), following three years of peace, to look for the people who had left years prior with a man named Zeniff to try to reclaim their inheritance in the land of Lehi-Nephi. Ammon was described as "a strong and mighty man, and a descendant of Zarahemla," and was asked to lead a search party of sixteen "strong men." Three of them were named (or titled) Amaleki, Helem, and Hem. The name Hem might be a title. At least, as Nibley points out, ?m means "chief servant" in Egyptian, especially in the title ?m tp n imn, "chief servant of Amon," i.e., the high priest of Thebes. To have been given this assignment of leadership, this Ammon must have been a highly trusted military officer and diplomat in King Mosiah’s court. After forty days of wandering, Ammon and his group arrived in the land of Nephi during the reign of King Limhi.
The other Ammon was the eldest (first mentioned) of the four sons of King Mosiah (Mosiah 27:34), who likewise left Zarahemla, but at the end of King Mosiah’s reign, to become missionaries to teach the Lamanites, again in the Land of Nephi. Because Mosiah was 30 years old when he was crowned and reigned for 33 years (Mosiah 29:46), Ammon could well have been born around the time the first Ammon led his group of 16 explorers to the south. If so, the second Ammon may have been named after the first highly trusted Ammon. They were at least contemporaries. There are also similarities between them: Just as the first Ammon had been sent back up to the land of Nephi because people (perhaps including that Ammon himself) had "wearied" Mosiah with their "teasings" (persistent provoking or prodding), this second Ammon and his brothers "did plead with their father," pestering him for "many days that they might go up to the land of Nephi" (Mosiah 28:5). The second Ammon may well have hoped for similar success as his namesake, the first Ammon. Among his successes, Ammon, the son of Mosiah, is the one who cut off the arms of the Lamanites while saving the flocks of King Lamoni and converting him (see Alma 17). He also converted and led the Anti-Lehi-Nephis, who were eventually called Ammonites (Alma 56:57), north into the land of Jershon.