What am I, a Photographer, an Artist, or both? (I will ignore, with your permission, the possibility of "neither"). In an attempt to simplify the analysis, I will define four points on a continuum.
These span from a "pure" photographer to a "pure" artist. From Photographer-Photographer (PP) to Artist-Artist (AA) through Photographer-Artist (PA) and Artist-Photographer (AP).
The epitome of a PP would be someone working for the National Geographic. Whether professional or amateur, the PP is most interested in making the perfect photograph. This would be distinguished by excellent technique, good colour, fantastic lighting, mastery of all the ways to make a really "wow" photograph. I believe 95% of all photographers fall into this category or wish to. Most online photography forums cater to this population (and financially speaking, this makes perfect sense).
The AA, at the the other extreme, is first and foremost someone wanting to express himself through Art. He may use the camera as a way to make studies or use it as part of the work. He does not define himself as a photographer at all.
With the PA and AP, things become more subtle.
The PA is in love with photography. In this respect, he may not be any different from the PP. I believe, however, that the PA is also interested in the philosophy of photography. In addition to the love of making photographs, he is constantly in awe about the nature of the photograph. He has read Barthes' "Camera Lucida" and is amazed with the uncanny meaning photographs give to life and death. He has also read Benjamin's views on photography. He constantly questions himself about the connection between photography and reality and is fascinated with all the questions that photography raises. The PA is also an Artist and has swallowed books on Art in an attempt to understand what it all means. He wants his Art to express himself using photography and nothing else (except text, maybe, which is a different topic). He believes photographs need to show more than what is there.
The AP on the other hand, is first and foremost an Artist, and only then a Photographer. He has probably studied in Art school before using a camera. He is less concerned with maintaining an indexical relationship between picture and reality. The photograph is primarily a tool for self expression, and he is more likely to experiment with other media in conjunction or instead of the camera. He could use photography without taking photographs via appropriation, he can use photography as a canvas on which to paint. He will define himself as an Artist.
So where am I on this continuum? It should be no surprise to the reader that I see myself today as a Photographer-Artist. I may find myself one day moving on to "the right", towards the AP, but one way or the other, I do not see myself abandoning the camera.