In the manga, during the first duel against Kaiba, Kaiba uses the Blue Eyes White Dragon which he stole from Yugi’s grandpa (he didn’t even draw it from the deck, the bastar had hid it somewhere and just pretended to draw it when he was starting to lose). He didn’t have any other Blue Eyes White Dragon at this point. Also, they weren’t using holograms, but images of the monsters were manifesting because the Millennial Puzzle had turned this duel into a shadow game. Anyway, the dragon refuses to fight for a cheater and self destructs. Yugi then uses Monster Reborn to summon the Blue Eyes White Dragon from Kaiba’s graveyard on his side of the field and beats Kaiba with it, then brings it back to his grandpa. That’s where panels of Yugi holding this card makes sense. There are then many chapters that happen without Seto Kaiba or the cards appearing, until he returns to challenge Yugi’s grandpa and that’s where the animated series picks it up.

It’s an alternate universe

Probably because the dark magician would just look like some random homeless dressed in weird robes, sifting through garbage.