After some flicking through my DP Pokedex guidebook and researching on Bulbapedia, I think I've discovered some innacuracies in the "Form differences" article...
Following is a summary I wrote of the definitions of each specific term. Please note than when I say "Official term" below I mean CONFIRMED AND IN USE BY NINTENDO.
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“Form” with a capital F
The term “Form” is an official term and refers to differences between individual Pokémon of the same species.
In order for a variant of a Pokémon to be recognised as a differing “Form”, the variant must have an official name. For example, Burmy’s Forms have the official titles of “Sandy Cloak”, “Plant Cloak” and “Trash Cloak.”
Temporary Forms
‘Form’ sometimes refers to temporary changes/morphs in physical appearance. These changes can be purely aesthetic as with Burmy, Deerling and Sawsbuck but in all other cases they also affect stats, types and/or move sets.
The triggers that cause these differences include weather, the environment, abilities, the current seasons or a trigger the player elects to activate purely for the Form change (e.g. Rotom).
Pokémon with this type of Form difference:
Castform
Burmy
Cherrim
Rotom
Darmanitan
Deerling
Sawsbuck
Permanent Forms
Form with a capital F can also refer to permanent variations between members of a species that are purely aesthetic with the exception of Wormadam, whose type, stats and move pool is affected.
Pokémon with this type of Form difference:
Shellos
Gastrodon
Basculin
Wormadam
“Forme” with an e
The term Forme (with an e) is an official term referring to temporary changes in physical appearance in Legendary Pokémon only. Like with “Form”, all Forme variations have an official name.
Forme can be changed using a method unique to that individual Pokémon. Deoxys, for example, changes between its Formes by coming in contact with different meteors. These changes affect stats, type and learnable moves.
Pokémon with Forme differences:
Deoxys
Giratina
Shaymin
Meloetta
Form (unofficial term)
This kind of “form” is not used officially, and is therefore spelt with a lower case f. It refers to just two Pokémon: Arceus and Genesect.
Arceus will change type and colour based on the Plate it’s holding due to its ability “Multitype”. (Its signature move “Judgement” may also change type but please note note that this is a mechanic of the move itself and not Arceus.)
Genesect will merely change colour based on the Cassette it’s holding. (While the move “Techno Booster” may also change type to match the Cassette, please note that this is a mechanic of the move itself and not Genesect.)
Variants (unofficial term)
Variants within a species are permanent aesthetic differences between individuals. This includes Unown and Spinda.
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Confused? Good.
if my definitions above are correct (feel free to point out if they're not) then I believe the "Form differences" article is extremely inconsistant, switching back and forth between "Form" and "form" or "Forme" and "form".
I think the article could be restructured, perhaps to have "Forms" and "Formes" listed seperately.
Feel free to also discuss Form differences and how confusing this all is! 
