The official terms are smooth coat and long coat. They are the same breed genetically, but they are judged in different categories in dog shows. A smooth coat only means that it has short hair, the hair can actually be soft and smooth or wavier and coarser to the touch. There is no difference between a long coat chi and a smooth coat chi, except in the look.
More on Are short hair and long hair chihuahuas the same breed?
Tags: Breed Info, Genetics, Grooming, Long coat, short coat