Maybe I don't so specifically agree on the "without caption" part of it. Sometimes the caption and/or title is a part of the piece. Not all the time, but sometimes.
I think intent is in no way the determiner. It is the way it is used/presented that makes the determination. Is it there simply to be a photograph, or does it exist as a photograph primarily in order to serve a purpose other than this?
The line is blurred all the time. Documentary pix often blur the line, and sometimes even photojournalism, especially when viewed in retrospect. Additionally, you also see work that was originally commercial becoming fine art at a later date...but as I said, it is the specific use that is the determiner, not the original intent.
As an example of how I think on the issue: The Ansel Adams shots on the covers of his books are commercial, though they were originally intended as fine art. In this case, the shot is used to make the purchase of the book appealing; not solely to display the photograph. The shots within are fine art. They are placed there to be viewed as photographs. In his technical books, many of the photos that were originally fine art are used as instruction aids. Original intent, or the actual content or style of the photo has nothing to do with it. It is the use that matters....but not that it really matters what the definition is anyhow....
Are the shots on the covers of AA books photographs? I don't think so. For me a photograph is a print, made by the photographer. Anything else is an image, including a reproduction of an AA print. Having seen original prints I have great difficulty in calling a copy a photograph as if it were made by a photographer. Of course that's my personal take, and it is pretty old school. You can find people that believe a cell phone image is a photograph, and I can't say that they are wrong, just that I disagree, if that makes any sense.