Pokémon Counterparts
Pokémon counterparts are specially colorated versions of Pokémon counterparts that are adventitiously encountered in the wild and—more conservatively so—obtained from Pokémon-giving NPCs.
Compared to other Pokémon MMOs, Pokémon Revolution Online is not multitudinously diversified in the array of special counterparts available; aside from the traditional shiny counterparts, special counterparts are more commonly obtainable as temporary event-thematic Pokémon than any regularly encounterable counterpart of wild Pokémon. Moreover, they do not bear any inherent statistical enhancements; they merely have an aesthetic distinction from their regular counterparts.
Shiny Pokémon are also the only special counterpart that each Pokémon has a version of; event-temporary ones are tailored to a specific assortment of Pokémon, as outlined below.
Shiny Pokémon

In addition to their distinctive coloration, shiny Pokémon are also identifiable by the golden S emblem; see the image to the right for a pictorial illustration.
Wild Encounters
For wild-Pokémon encounters, their odds are fractionally identical to those in the handheld games at 1/8192 (0.0001220703125%).
When hotlinked in the chat, their link is purple-colored to differentiate it from their regular counterparts; for example, a shiny Pikachu would appear as <Pikachu> when hotlinked.
Any wild-Pokémon battle initiated by an NPC script will not have a shiny chance; this includes even catchable Pokémon encountered via Headbutt_Trees, Diggable Crevices, Excavation Sites, and overworld-interactable Pokémon (such as the occlusive Snorlax on Route 12#Roadblocking Snorlax).
NPC-Given Pokémon
While the wild-battle-initiator used by NPC scripts has no shininess chance, Pokémon that are directly given by NPCs can still have chances if the RNGs are configured within the scripts for it; examples include fossilized Pokémon regenerated by the fossil-reanimators, some boss-prize Pokémon, and abandoned Pokémon.
Because these Pokémon are given much more infrequently than wild Pokémon are encountered, they tend to have varyingly lower shiny-chance odds than the standard 1/8192 rate of wild Pokémon.