Samuel identifies the Messiah as the Redeemer. This is the Atoning Messiah, not the Triumphant Messiah. The Nehorites might have retained a belief in the Triumphant Messiah at the world’s end as described by brass-plate prophets. (See “Excursus: Religion of the Nehors,” following Alma 1.) The conflict in Nephite society has always been this understanding of the Atoning Messiah, and the debates over the Messiah have centered on his mortal mission, not his second coming.
Samuel does not directly reference Nephi2’s teachings to these same Nephites (he was probably not in Zarahemla at the time to hear them), but both prophets have the same intention: “And as many as should look upon that serpent should live, even so as many as should look upon the Son of God with faith, having a contrite spirit, might live, even unto that life which is eternal” (Hel. 8:15).
For Samuel, the important phrase is “believe on his name… have a remission of [sins].” For Nephi, it is the Mosaic “look upon the Son of God… [and] live.” In each case, the prophet invokes the prophesied Messiah in his role as Redeemer. The message of both is redemption from sin and death. For both, the key is belief in the Savior, either through the sacred acceptance of the name or the symbolic “looking.”
Neither the name nor the serpent symbol is the effective element. Both stand for our actions. For this reason both prophets emphasize the necessity of our own repentance, explicitly in Samuel and implied in Nephi’s “having a contrite spirit.”