Oh, you can definitely have fiction of any kind that includes commentary! That's not the relevant point to whether or not it's fanfiction. What I'm trying to get at is that a story can be related to another source, through these other methods such as critique and parody, without necessarily being fanfiction of that other source.
A sci-fi story with all original characters that deconstructs tropes used in Star Wars would not be, whereas a sci-fi story with Luke and Leia that deconstructs tropes used in Star Wars would. Wicked makes sense as Oz fic; 30 Rock does not make sense as SNL fic. And so on.
In terms of RPF versus "original fiction which includes real elements", I think the relevant question is whether there's something fictionalized in the story. Mitchell Hundred's NYC does not exist; Olbermann's NYC does. Character!Stephen does not exist; real!Stephen does. Thus, a story in which Olbermann and r!Stephen have a conversation which is entirely made up by the author would count as fanfiction; a story in which an original character fangirls c!Stephen would also count; but a story about an original character who fangirls r!Stephen or Olbermann would not. (Unless she meets them, and they end up becoming bestest friends or going on Magical Space Adventures or what have you. In which case it's back to being fanfic, if probably Sue!fic.)
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A sci-fi story with all original characters that deconstructs tropes used in Star Wars would not be, whereas a sci-fi story with Luke and Leia that deconstructs tropes used in Star Wars would. Wicked makes sense as Oz fic; 30 Rock does not make sense as SNL fic. And so on.
In terms of RPF versus "original fiction which includes real elements", I think the relevant question is whether there's something fictionalized in the story. Mitchell Hundred's NYC does not exist; Olbermann's NYC does. Character!Stephen does not exist; real!Stephen does. Thus, a story in which Olbermann and r!Stephen have a conversation which is entirely made up by the author would count as fanfiction; a story in which an original character fangirls c!Stephen would also count; but a story about an original character who fangirls r!Stephen or Olbermann would not. (Unless she meets them, and they end up becoming bestest friends or going on Magical Space Adventures or what have you. In which case it's back to being fanfic, if probably Sue!fic.)