Antelope

Neither antler nor horn, the antelope's cranial decorations are unique to them.  Natives of a large swath of western North America, pronghorn antelope have unique "horn sheaths."  They have a bony component and are shed, like antlers of deer and elk, but they also have a horn component (notice that I purposely avoided the term "horny component," yet still found a way to mention it), made of the same keratin as hair and cow and rhino horns.