Hey, I know the thread can get frantic so I posted it here too:
Game Freak is extremely particular in its wording.
Formes always have different stat layouts (. Giratina, Shaymin, and friends? Those are all formes.
Forms, don't. They're almost purely aesthetic. The only form to receive a difference is Castform, who changes type with its forms but not stats.
But wait, you say, what about Rotom, Wormadam, and Darmanitan?
Here's where game freak gets silly: None of them are referred to as formes or forms. Wormadam? Those are just cloaks. Darmanitan? Modes. Rotom? <word> Rotom
So only when a legend changes form and gets stat redistribution, is it called a Forme.
Seriously, check the Pokedex. The Basculins are specifically called Red/Blue-Striped Form. The Cherrims are overcast/sunny form. Unown is One Form (har har). And so on.