Horns, antlers - they're pretty much the same thing, aren't they? Oh, young one - how little you truly know...
Leaving aside rhino horns (which are made entirely of keratin, the same material that comprises human hair and fingernails) and the peculiar little bumps you find on the heads of giraffes (their official name is ossicones), horns and antlers primarily differ because while the former are permanent features, the latter are grown and shed annually.
With this being the case, it is very rare for an animal that loses a horn - which consists of a keratin covering and a core comprising real bone- to regrow the lost appendage. When a creature loses an antler - which is made up of mineralised cartilage - it'll regrow when the animal sprouts its next set of antlers the following mating season.
As for the animals that sport true horns, they cover a wide range of creatures taking in the countless species of sheep, cattle, goats, antelope and goat-antelope (this rather strange grouping includes equally strange animals such as the chamois and the takin), not to mention muskox (which aren't true oxen) and the world's fastest land animal - over a distance - the pronghorn.
Antlers, on the other hand, are only found on deer, ranging from the tiny pudu from South America to the gigantic moose. Not only that but, with the exception of the reindeer, it's only male deer that sport antlers which they use in fights to establish sexual dominance.