Not necessarily. 'Reindeer' could be purely imaginative or inspired by real-life but with significant alterations. It really varies depending on the context and the author's intention.
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.
Reindeer is typically not based on a true story. It might incorporate some common themes or tropes, but it's not a reflection of actual events. It's the imagination of the creators brought to life on the screen or in the pages.