The main differences are in their expressions and some minor details of personality. In the manga, Deku might seem a bit more intense, while in the anime, he's sometimes presented a bit softer.
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Deku might be completely shocked at first. Since Bakugou has always been so aggressive towards him, he would never expect such a confession. He might just stand there, mouth agape, not knowing what to say.
His friends could come to the rescue. Bakugo, for instance, might use his explosive power to break into Toga's hideout. He's always been competitive with Deku, but he also cares about him deeply.
In 'deku meets future deku fanfiction', perhaps the future Deku warns the present one about upcoming threats. He could tell him about villains he'll face in the future and how to defeat them. This would give the present Deku an edge in his battles and also in his growth as a hero.