One of the problems with science fiction is that there is no secular term for the soul. It's a religious concept with no scientific basis, but artistically it conveys a very important idea that I think sometimes gets lost in sci-fi. It's a simple term for an important idea that gets rejected out-of-hand because it's a religious idea, but it actually matters a great deal for non-religious reasons.
In essence, soul is an easy shorthand for the breadth of one's inherent, individual being-ness. To avoid the kneejerk associations that sci-fi fans have to the word "soul", I tend to use "continuity of consciousness" to try and explain this idea. But a lot of times people still don't quite seem to grasp it.
In essence, there is a tendency in sci-fi to think of people externally. A person is their demonstrable factors. Their appearance, their personality, their memory, their experience, all things that can be interacted with or recreated through the magic of super-science.
If you clone Joe, then the result is Joe! We brought Joe back to life through cloning. Now Joe is here with us again. And if we clone Joe again, we get two Joes! Isn't that amazing? And they're both Joe!
But.
Like.
We don't think of people internally. Are they both Joe? Is either of them even Joe? Or are they brand new people saddled with Joe's memories and personality and history?
What happened to Joe? We're only thinking about Joe in terms of our perspective as people who are not Joe, but what was Joe's experience? Did he actually die, and then wake up in a new clone body? Is his continuity of consciousness preserved? Did he actually experience coming back to life? Or did Joe die, and now Joe is still just dead. And there's been a new consciousness created to inhabit the clone?
What does this experience look like from Joe's perspective? Not Clone Joe. Original Joe.
Severed from its religious meaning, this is what the soul is an artistic shorthand for. Joe's "soul" is a simple and easy way of conveying the question, what actually happened to the inherent consciousness/personhood/continuous thinking existence of the true Joe? Does the clone share the same "soul" or does it have a new "soul"? Do their consciousnesses continue from one to another or are their consciousnesses separate?
Even calling it "consciousness" doesn't fully convey this idea. Because they can have different answers for that. The clone may feel that their consciousness extends back throughout Joe's death and life, while the original Joe's consciousness nonetheless ended at death. There is no secular term for the inherent quality of a continuity of individually existing, in and of itself.
And because there's no secular term, we just don't think about it.
But I do. I think about this every time I'm presented with a clone or a time-travel duplicate or a parallel universe counterpart, and told by the story to treat them as if they were the same. If this character does not share continuity of the original's consciousness, then they are not the same. Even if all other features are identical.
And I don't know how to express that with words.