Albinism is the "congenital absence of any pigmentation or coloration in a person, animal or plant, resulting in white hair and pink eyes in mammals. Out of the three conditions we are talking about this seems to have the largest variety of species affected. All three conditions are caused by a recessive gene. None of these animals are new species they are exactly the same as a normal animal.
A piebald or pied animal is one that has a pattern of pigmented spots on an unpigmented (white) background of hair, feathers or scales. In some animals it is a dominate trait shuch as Holstein cattle and pinto horses. The gene is recessive other animals such as deer, squirrel, and coyotes.
Melanism is a development of the dark-colored pigment melanin in the skin or its appendages and is the opposite of albinism, but unlike albinism there can be color variation. They can be all black or just noticeably darker then a normal animal. The frequency depends on species it is fairly common in squirrels in some parts of the country, but is extremely rare in deer or bobcats. For example only 1 in 100,000 deer will be Melanistic.