*Membership spots not really limited!
The standard way to "break into" the comic-book industry for YEARS has been to write an "inventory story" about an established, long-running character like Captain America or Supergirl, and send it to the editor of that book. An"inventory story" is a pre-written script that the editor keeps in his filing cabinet (or nowadays on his hard drive) for emergencies. When Rick Remender can't make his Cap deadline, the editor reaches into his file and looks over the list of a half-dozen or so inventory stories. These are one-shots that are not heavily continuity-based, so they can be run "any time." The editor selects one and then hires an artist to draw it (or perhaps has the regular-series artist do it). The writer is then paid for the work.
Significantly, the unsolicited inventory story was not written with permission. It was written, most of the time, by a fan. That fan is writing, by your definition, fan-fic, because he did not have permission to actually write the thing before he wrote it. AFTER having written his fan-fic Cap story, and being told by his friends/family it was good, he submitted it to the Cap editor. Later, the editor chose to publish it. Thus this item which by your definition started out as fan-fic, became part of the canon.
So, they're not as distinct as you are making them out to be.
I don't think that's happened in at least a decade.