Today I heard a speaker use the phrase "this person", referring to the subject-person of the story they were telling, and I heard it as (that person). Between the words “this” or “that” in context with the phrase and story-tense, which should you use.
The difference between "this" and "that" is that "that" is further/far away from "this". So, let's say you're reading a story, from a book, and you have that book placed in front of you, and you're speaking about a person mentioned in the story of that book, it would better to say "this person", whenever you mention a persona of that story. "That", as in "that person", is used when referring to a person not close to you, or close to your perspective.
Also, the subject-person of the story is often addressed with "this", instead of "that".
What I mean with that is, assume there's another persona in that story who's not the person you mention the most, it would be better to use "that". I'll give you an example:
"So, this person (subject or person talked about frequently) went to the market, and met a strange person, who looked really scary. That person (the strange person) was not known to the inhabitants of that city."
So, that's what I mean with perspective. So, which one should you choose? That depends on the context, as shown above.
Very often, people will use "this" in place of "a" to mean a specific instance of a thing, previously not mentioned. For example, "I have this problem with spiders." Or, "There was this person walking down the street."
It's generally considered an informal, conversational usage.