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The theme for the games is light.
>New Snap = Illumina Pokemon
>Brilliant Diamond = Time + Light
>Shining Pearl = Spatial Dimensions + Light
>Endgame Episode: Shadow Platinum = Distortion in the absence of Light
>Legends Arceus = Light as a means of attaining perfection
There are new forms in BDSP but not really in Legends Arceus. In Legends, the "forms" are a result of Arceus empowering Pokemon with its light and are not permanent, physical changes like D/GMax or Mega Evolution.
Many details about BDSP are being purposefully hidden. I can say that the games are not like ORAS. ORAS made a big deal about its new content and incorporated it into the story. For the most part, BDSP treats the new content like the new forms and features were there from the beginning. This makes the games appear very close to the originals on the surface. The games also bring back basically everything except for the true National Dex and certain regional gimmicks. The event mythicals like Shaymin, Darkrai, and Arceus are in the games. Legends Arceus will be used to obtain Manaphy in BDSP in a way similar to how the Ranger games were used in the past. The Legends Arceus "empowered" forms are not the new forms in BDSP and the new forms in BDSP are not in Legends.