I think you’re confusing the Amulet of Mighty fists with the hand wraps. (AMF) applies to all unarmed and natural attacks a character can have, but it can only go up to a +5 total enchantment (it doesn’t need the initial +1 to add special enhancements like flaming however). The hand wraps allow you to fully enchant your unarmed strikes almost exactly like a regular weapon but ONLY your unarmed strikes (some DMs even go as far as to say attacks with fists specifically but that’s a very niche situation if you’re arguing over that) TLDR: amulet applies to all natural and unarmed attacks but only up to +5, wraps only apply to unarmed attacks but go all the way to +10 total