According to their respective wikis, covered horns is for horns under hats and other headwear whereas horn cover is for "detachable covers". This doesn't make sense since it seems to imply that headwear is not "detachable".
I think the intent is to distinguish between horns underneath hats like post #9618371, and coverings made specifically for horns like post #2507157. If so, it needs to be made more clear in the wikis. Also one or both should be renamed. "X cover" and "covered X" are too similar and too close to being synonymyns in ordinary language to expect users to keep them seperate. One possibility would be to rename covered horns to horns under headwear, in order to parallel horns through headwear. Or, since horn covers could be considered a form of headwear, horns under hat, horns under hood, etc.