The only thing we have seen so far are incendiary, cryo, and electric weapon mods.
If it works anything like Skyrim
-Incendiary weapon mods will cause fire damage over time, cause more damage to targets already on fire, and possibly cause the enemy to freak out and run away when their HP gets too low.
-Cryo weapon mods will drain AP, slow target movement speed down by 50%, and temporarily paralyze, aka freeze a target, once their HP gets down low enough.
-Electric weapon mods will likely do something like double damage to robots and power armor, and possibly vaporize a target once their HP gets down low enough.
Fallout shelter did have armor piercing weapons, but those were treated as a type of weapon, rather then a type of ammo, and were the best kind of gun below the unique named legendary weapons in Fallout Shelter.