I think the point when it starts feeling like fanfic with my own work is when I'm writing things that aren't intended to be canonical. It's definitely the kind of thing where you can make arguments either way, though. I'd be inclined to say "if the author says it's fanfic, it's fanfic", but YMMV. It's the same kind of thing as debating whether stories based on, say, the Bible count as fanfic or not - it really depends on how narrowly or broadly you define fanfic, and what you pick out as key features of it, and to some extent on what the story itself is doing.
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I think the point when it starts feeling like fanfic with my own work is when I'm writing things that aren't intended to be canonical. It's definitely the kind of thing where you can make arguments either way, though. I'd be inclined to say "if the author says it's fanfic, it's fanfic", but YMMV. It's the same kind of thing as debating whether stories based on, say, the Bible count as fanfic or not - it really depends on how narrowly or broadly you define fanfic, and what you pick out as key features of it, and to some extent on what the story itself is doing.