For me, they overlap significantly. I'm not prepared to say that they're identical, because writing 750 words on Hilbert spaces for an encyclopedia and writing 750 words of short-short story are not at all similar for me. But, for example, telling a story about my cousin and telling a story about one of my characters are not all that dissimilar. I think most people tell stories about their family and friends naturally, without necessarily identifying what they're doing or how they're doing it, so it's harder to apply it to fictional characters because it feels like your ordinary conversational stories are just saying what really happened, and with fiction, that's not an option.
But think about the times when you've told a story and it's fallen completely flat. You thought it was hilarious, and the person you were telling it to didn't find it funny at all. (See also: cool, sad, interesting, etc. This doesn't just apply to humor.) There are lots of reasons for that, but one of the big ones I've run into is "you had to know so-and-so." Sometimes you can fix this in advance by starting the story with something like, "My aunt has always really liked tap dancing," or, "My friend and her father-in-law never really got along," and then your listener has the background they need for the story to make sense. Other times, you end up deciding, with regret, that you're not going to be able to condense years or decades of friendship or hundreds of books or movies or work tidbits worth of common reference into a short enough span to be able to convey the humor, so you save the story for an audience that does know the people or the common reference points.
Many people do this automatically. I think most of us do. Sometimes it fails, but often we can learn from those failures to tell different stories to a given person, or tell the same stories differently.
One of the great things with fiction, of course, is if you write a story and give it to someone to read and they say, "I don't get why the protagonist did this," or, "I don't get why it was cool that the protagonist did this," you can sometimes fix that. You can rewrite the story in a way that you can't replay a conversation. Until it's published, you're not stuck with forgetting to put in the part about how far it is to Mankato or what your roommate said the first time you forgot your keys.
So what you're doing is trying to pick out the right details. And you do that in almost any type of writing. With my encyclopedia article on Hilbert spaces, for example, if I spent most of the 750 words talking about what it means for something to be countably infinite, I will have picked the wrong detail for my purpose, or if I use the space to list examples over and over again without explaining why they are examples and something else is not an example. If you're writing up a work procedure for a training manual and you talk a lot about how your specific boss likes reports for a completely different procedure organized differently, that's the wrong detail.
How do you know if something is the right detail in fiction? You reread it and see how it goes. You give it to someone else to read, and they say, "Um...what was I supposed to get from the fourteen pages about her hats? Because I really didn't get what that was doing in there when the hats didn't turn out to be important to the plot or the character or...anything really." You read a lot of fiction and pay attention to which details the authors you like have included and what they're doing in a paragraph, in a scene, in a chapter, in a story.
I wonder if people tend to organize their thinking for approaching a large fiction project similarly to the way they organize their thinking for approaching a large nonfiction project. I know I do, but this is one of the times I don't really want to generalize from one example. I know that there are people who outline very formally and others who outline informally and still others who don't like to outline at all. I'm in the middle group for both fiction and nonfiction, but I'm wondering if others see it the same way. Also I like to do a bunch of research, think about where I might be going, outline informally, do a bunch more research, and then fix all the ways I was wrong before about where I thought I might be going. I like fixing the ways I was wrong before. It's so soothing! Hey, I was wrong, and the sky did not fall in! I was wrong, and now I am not-wrong, hurrah! Or at least less wrong! Hurrah!
If anybody else wants to talk about anything they've found useful across the fiction/nonfiction boundary, my friend might find it helpful, and I might find it interesting. Please feel free.
If you haven't written a lot of fiction, you probably can't write good fiction right off the bat. This is not anything bad about you. It's just that it's a skill, like anything else is a skill; unless you're a Mary Sue, you don't expect to be able to pick up your first wind instrument ever and sound like Louis Armstrong on the first day. So if you've mostly written nonfiction and you're making your first venture into fiction, when the little voice says, "I can't write fiction, I don't know how," you can answer it cheerfully, "No, that's true, I don't. But I can learn." You hit a lot of wrong notes when you're learning a new instrument, and if you're trying something like the oboe, you break things a lot and your tone is painful to all listeners for awhile, and that's okay. Practice really does help. You don't have to start out knowing everything you need to know. It's like the rest of life that way.