The different colourations of Shiny Pokemon is merely Game Freak Logic. From this source, you can see that Shiny Pokemon were called alternate coloration or rare coloration Pokemon, indicating that it used to represent a very rare specie within its species. The drastic different of the shiny Pokemon is essentially Game Freak's choice since we can't really relate it much to real life since not all Pokemon are animals, evident by Pokemon such as Rotom, Pallosand, or Klefki (hence the name Pokemon derived from "Pocket Monsters" )
Yes, it is logical that in terms of animals, that different textures of skins etc. of an animal represents a rarer specie, but then again, the only different in terms of physical appearance between a regular Pokemon and it's shiny-counterpart of the same gender is just the colour. Simply, it's just used to distinguish a rarer specie.
In newer games, a Pokemon is simply calculated to be shiny based of "Personality Values" and incorporates the original trainer's Trainer ID number and Secret ID number to do so. As of Gen III, the mathematical breakdown of a shiny Pokemon can be found here.
Hope I helped! :)