Photography is a lot of different things to a lot of different people. So is 'art'.
Photography is a specific act: painting/drawing with light.
Art, insofar as it is relevant to the subject at hand here, is defined by the Oxford Dictionary as, inter alia: "The expression or application of human creative skill and imagination, typically in a visual form such as painting or sculpture, producing works to be appreciated primarily for their beauty or emotional power."
That's about as good as it gets. Art also requires an 'act' or sorts; it doesn't just come into being magically, but needs a 'doer'. One could also argue that it requires intentionality. Meaning it requires desire to achieve something that qualifies as art; though it may not actually be thought of that way by the artist. And, as far as I'm concerned, the intentionality required is confined entirely to members of the human species.
"Fine Art Photography" therefore—and I really think we can lose the "fine"; unless we want to juxtapose it with "gross" or something like that—would be photography as art, that is using the techniques provided by the tools available to us for painting with light for the artistic purposes in the definition; that is to display/highlight/enhance of the esthetic qualities of the photographed subject and/or the evocation of emotion in someone looking at the image.
What then are the subjects of "fine art photography"—as opposed to whatever other photography there may be? Well, basically anything; mainly because there cannot be any limitation on what can be painted with light in such a fashion that its esthetic qualities become the focus of an image.
(to be continued...)