In tandem to Torym's answer, in the anime and manga every separate Pokemon is different in some small way, even if they are the same species. These usually relate to colour changes such as the Pink Butterfree or markings, such as Mays Bulbasaur having heart markings on it's head unlike Ash's which is plain. In the games however, only some Pokemon have differences in appearance to others of their species. The main aesthetic differences are: Gender differences (for example, a male Gyarados has blue whiskers and a female Gyarados has white whiskers), Forme changes (For example Flabebe has multiple different colours, or Giratina has a different forme depending on whether it is holding the Griseous Orb), special Pokemon (for example the Spikey-eared Pichu from Pokemon HeartGold and SoulSilver), and Spinda (every Spinda has a unique pattern of spots generated by it's IVs and personality). Other differences are non-aesthetic, things such as IV's (individual values randomly generated upon encountering the Pokemon or hatching the Pokemon's egg), EV's (effort values which a Pokemon obtains upon defeating other Pokemon), Nature (a randomly generated nature that affects the Pokemon's stats), Ability (some Pokemon have multiple abilities), and lastly a PID (a hidden value that is generated based on the Pokemon's Ability, Nature and IV's). Those are pretty much all of the differences between Pokemon in the games and anime. Of course, there are moves too but that is an obvious one.