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.
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.
Well, obviously Deku in two forms - the younger and the older version are the main characters. The younger Deku is the one who is still growing and learning, while the older Deku has more experience.
As of now, Deku is very much alive in the manga. The plot hasn't reached a point where he meets such a fate. Usually, main characters like Deku have significant story arcs and aren't easily killed off.
Another possibility is that a new villain emerges as a result of the time - travel or whatever mechanism brings future Deku to the present. This villain could be from a future where Deku's actions (or inactions) have led to a more dangerous world, and he travels back in time to stop Deku from making those mistakes again. However, his methods are extreme and dangerous, making him the antagonist of the story.
He might cry a lot. Deku is very emotional, and being cheated on would be a very painful experience for him. He could also get angry, which is rare for him, but this situation would be so unjust that he might not be able to hold it in. He'd probably start to question his self - worth too, thinking that there was something wrong with him that made his partner cheat.
Another plot might involve the older Deku being from an alternate timeline. He shows the younger Deku different ways he could have developed his skills and relationships, which makes the younger Deku reevaluate his own path as a hero.
Deku might be initially shocked. He's used to Bakugou's aggression, but an actual injury is different. He could be in pain and disbelief at first. Then, he might try to downplay it, especially if he doesn't want to cause trouble for Bakugou, because Deku is generally a very forgiving character.
In the manga, Deku experiences various ups and downs. He not only becomes stronger physically but also matures emotionally as he takes on greater responsibilities. There are also many unexpected plot twists that shape his journey.