Like Mega Pokémon, Shadow Pokémon are an alternative form of a Pokémon. However, there are two kinds of Shadow Pokémon:

A) Pokémon with a shadowy Aura around them, which may be Purple or Black. These are the more common types of Shadow Pokémon in canon.

B) Pokémon with inverted coloration, or at least the same colouration (or similar) to a Shadow Lugia. These are more common in fanart than their weaker breatheren.