A "functional form" is a Pokémon form that changes something about the way that Pokémon behaves mechanically (e.g., in battle): a different type combination, different base stats, different available moves, etc.. It is different from a "cosmetic form" that only changes the Pokémon's appearance but otherwise leaves it mechanically unaltered.
Regional forms are a subcategory of functional form specific to a given region (and usually entirely replacing the original form in that region).
