As described on their original DOJO!!! post, Battle Cards would have summon a random non-playable character to aid the player who summoned him/her in a similar fashion to released Assist Trophy characters, with the only difference being that only a KINGDOM HEARTS character (or, in a sense, a Disney character) would have appeared. Battle Cards would have come in red, blue, green, and black colors. The DOJO!!! post also implied Battle Cards would have caused other multiple effects on the summoner, as that is how the actually worked in their source game, however, developers would later clarified all Battle Cards were only meant to summon a character and that the color of the card would have nothing to do with its effect.
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Cards first appeared in the game KINGDOM HEARTS: Chain of Memories where they were used by Sora and Riku to fight and proceed through Castle Oblivion. There are two types of Cards: Battle Cards and Map Cards. Battle Cards, in turn, are divided in Attack Cards, which contain one strike with a Keyblade (they are colored red); Magic Cards, which let Sora use a spell or use a summon (They are colored blue); Item Cards, which restore attack and magic cards after use (they are colored green); Friend Cards, which summon one of Sora's party members once retrieved and used (most likely the color of card that will summon characters in SSF2, they are colored green too); and Enemy Cards (enable a status effect, which can change Card Value, increase speed, and make Sora invulnerable to certain elements. They are colored black). There are other types of Cards but are not in the Battle Cards line.
A rumor among McLeodGaming community was that a summoning item in the form of card would appear as an item. This led to the belief of Yu-Gi-Oh! cards as an item in SSF2, which spread a discussion all over the SSF2 community. Nothing was official until the confirmation of Battle Cards.
Since the Battle Cards are no longer a part of SSF2, it is still possible that the characters that were planned for use of the Battle Cards could still be used as Assist Trophies. However, because they are all a part of the same franchise, not every character could be included.