Well - part of the confusion comes from the fact that the Horn Shark - isn't just a single species - but rather a genus of at least 8 different species. Some scientists actually are preposing that the Genus Heterodontus should be split into several different genera - instead of just one. Heterodontus - which means different teeth - which refers to fact that they two different types of teeth in the mouth.
Common names vary from - Horn Shark, to Bullhead Shark, to Port Jackson Shark, to Oystercrusher Shark.
Generally speaking the species of Heterodontus are considered to be temperate to sub-tropical species- usually found in water temps between 55-80F. But that varies depending on the actual species in question.
In American(North, Central & South) waters - there is 3 known Species of Heterodontus. The California Horn (H.francisci) - is the largest of the American species reaching up to 4 ft in length. It is found from Southern California to the Southern tip of Baja. And it is the most common species found in North American Aquariums. The Mexican Horn (H. mexicanus), is found along the Pacific coast of Mexico and Central America. It grows to about 28-30". The Galapagos or Pervuan Horn (H.quayi), is found along the South America coasts of Colombia & Peru, as well as out to the Galapagos Islands.
In Australian Waters - there is 3 species of Heterodontus, The Port Jackson (H. portusjacksoni) is the largest species (at about 5.5 ft), and native to southern Australian waters. The Crested Bullhead (H. galeatus) is slightly smaller (at about 5 ft), and found in eastern Australian waters. The Zebra Bullhead or Horn(H.zebra) is found from Southern Japan to Northern Australia, and grow to about 4 ft.
There is also 2 species found in the western Indian Ocean. Both are little known and fairly recently discovered species, that seem to stay less than 3 feet in length.