The intertwining of religion and politics is evidence in the way Mormon defines the word “Nephites.” We know that that was the designation of the political entity, but Mormon expands that to be “the people of God.”
In contrast, the people of Amlici were designated by his name. Royal Skousen found that there were some spelling variations in the name, and that a name we will see later, Amalekites, may have been essentially the same name. In the manuscript, it appears that it was a hard “c” in name Amlici, and the emphasis may have been on the first syllable. Thus, it is entirely possible that they were the same designation.
While that might suggest that they were the same people, the timings and locations of the names suggests different peoples. However, what links them is the desire for kings. In Hebrew, the mlk root designates “king.” It appears that Mormon intentionally designates many peoples who desired a return to the monarchy, or otherwise represented a contention within Nephite society, with names using the mlk root. Thus, Amlicite (pronounced Amlikite) and Amalekite might be essentially the same name, but not because they represented the same people. Rather, they represented the same idea, and, therefore, Mormon gave them a name by which Mormon appears to have assumed his readers would understand that they were similar in their desires.