Basically fine art photography is defined by photography produced for aesthetic reasons rather than for as a commercial project.
aes·thet·ic
esˈTHedik
adjective
1.
concerned with beauty or the appreciation of beauty.
“the pictures give great aesthetic pleasure”
noun
1.
a set of principles underlying and guiding the work of a particular artist or artistic movement.
“the Cubist aesthetic”
com·mer·cial
kəˈmərSHəl
adjective
1.
concerned with or engaged in commerce.
“a commercial agreement”
synonyms: trade, trading, business, private enterprise, mercantile, sales
“a vessel built for commercial purposes”
2.
making or intended to make a profit.
“commercial products”
synonyms: profit-oriented, money-oriented, materialistic, mercenary
“a commercial society”
Of course there isn’t always a clear line between fine art and commercial art or photography. Once can appreciate great photography created for commercial purposes or use art created as a fine art project in an ad campaign or on a product.
But the term “fine art” refers the the original intent of the artist. Fine art photography’s client is the artist themselves and the viewers. No assignment or constraints are given by a third party.
In commercial projects a client give the photographer directions and guidelines for the project. These may be extensive or vague but the photographer clearly is bringing about the vision of the employee, not solely their own vision as it would be in fine art photography.
Is that really the only difference between fine art photography and commercial photography? Yes, basically the intent of the photographer. Working for themselves vs. others.
Fine art photography can be sold of course but that doesn’t change whose vision is behind the work. Fine art photography serves to share with the world the unique vision of the artist. Commercial photography exists to sell products.
Another element often assigned to fine art is the level of craftsmanship although when compared to the quality of commercial photography say in the world of fashion, this really is a rather mute point. But if you were to compare an Ebay snapshot created to sell some old leather books, then the craftsmanship levels do add into the equation. But craftsmanship alone does not determine fine art from commercial work, it is the intent and purpose of the work.