When giving a presentation or workshop I always ask if anyone in attendance has ever asked themselves this question. For the most part, only one or two people raise their hands. I shouldn't be surprised anymore, but I am.
I go on to explain that I have given this question a lot of thought and I have concluded that I'm both. I consider myself a photographer when I'm out shooting and an artist when I come back to process and post-process my images.
It's an important question to ask yourself. The answer may surprise you.