From SmashWiki, the Super Smash Bros. wiki
Battlefield forms are alternate versions of stages in Super Smash Bros. Ultimate which modify them to have a layout that matches Battlefield in size and shape, consisting of a single flat hard platform with three soft platforms in a triangle formation floating above it.
In the introduction of Ω form and Battlefield form stages in the E3 2018 Nintendo Direct, Masahiro Sakurai stated that all Battlefield forms will be identical, differing only in music and aesthetics. Despite this, stages that have the 2D flattening effect in the regular stages also have it in their Battlefield forms, which alters how hitboxes function.
Mob Smash uses unique versions of Battlefield forms. These versions are nearly identical to the standard versions, but also have moving platforms spawn above the main three soft platforms. These platforms move from one side of the screen to the other, carrying items to help the player during Mob Smash modes, and will appear more often when the player moves around a lot and uses many different moves.
Stages that have the 2D flattening effect on their Battlefield forms are typically banned for tournament use, as the effect significantly alters the function of hitboxes.
Fountain of Dreams is banned due to framerate issues.
Gamer is sometimes banned due to the camera angle differing from other stages.
Otherwise, Battlefield forms are treated the same as Battlefield and are struck alongside it when either are picked.