Time travel is a very common device in fiction and has been done in many different ways. Three common ways are:

• Multiple timelines: Going back in time creates a new timeline that splits off from the original timeline at the moment you arrived. You can make any changes you want to the new timeline since it's not the same timeline you came from, but it won't directly affect the present of your timeline.

  Examples: Avengers: Endgame, the Star Trek Kelvin timeline, probably X-Men: Days of Future Past, Homestuck, the way Doc Brown explains time travel in Back to the Future

• Single, fixed timeline: There is only one timeline, so going back in time brings you to the very same past that already happened, not an alternate version of it. You can affect the past, but you can't change the past, because everything you do to affect the past already happened as part of the past you originally came from. This type allows for the bootstrap paradox, i.e., causal loops.

  Examples: The way time travel works in general relativity, the first Terminator movie, Tenet, "-All You Zombies-" and its film adaptation Predestination, Homestuck, Harry Potter and the Prisoner of Azkaban, Bill and Ted's Excellent Adventure, Interstellar

• Mutable timeline: The timeline can "change". It's usually not clear what exactly this means, since normally "change" refers to something being different at two points in time, but this refers to an entire timeline changing without it just being "a new timeline is created". However, there are some clear ways to show that the story follows this way of time travel, like having characters change the past, and then showing how those changes affect the characters themselves. Sometimes it's ambiguous whether a movie follows this or multiple timelines.

  Examples: Looper, the way time travel actually works in Back to the Future, "A Sound of Thunder", Homestuck, Groundhog Day, Edge of Tomorrow

• The type that's inconsistent about which type it is: Any story that contradicts its own rules about how time travel works, depicts time travel working in different ways in different parts of the story with no explanation for why it behaves differently, or has the explicit rules of time travel be, "There are no rules," or "It works differently in different situations and it's too complicated to explain why."

  Examples: Doctor Who, Back to the Future by virtue of its previous two mentions, Homestuck, any time travel series that lasts long enough

Which of these do you like the best for fictional stories? This isn't necessarily which one you think is the most realistic, but which one you think makes for the best stories.