Over on Disphotic, Lewis Bush asks "Is There a Language of Photography?" I don't really propose to answer that question here, but rather to shed some light on it.
In any representational art there is the art object itself: the photograph, the statue, the painting. Also, there is the thing represented: the model, the mountain, the landscape. Photographs are, I think, unique in that they at least begin with an accurate representation of a real thing. A painting needs no actual model, although often there is one. A statue need not look much like the model, and indeed tends to be idealized or at any rate altered.
A photograph is like a story that is based on a true story, while a painting tends to lean more toward fiction.
In between the photograph and the model, there are some other concepts. The arrangement of masses and lines, perhaps, might be said to be a thing, something we can name and talk about and think about it. That thing, whatever you call it, is neither the photograph nor the model. Perhaps it's something that lies between the two. One might argue that there's a spectrum of things between the photograph-as-an-object and the model-as-an-object.
More on this later, but for now let us think about language specifically.
What does this have to do with a Language of Photography?
The point is that there's "language" embedded in all these layers, potentially. By "language" I mean pretty much anything that communicates something that we can, more or less, agree on. It doesn't have to translate into words, it can be an emotion, a reaction. When communication occurs, it's simply because the maker and the viewer agree to some extent on what it is that is communicated, and that, I consider to be "language" enough.
Since the photograph is first and foremost, based on a real thing, some of the visual elements are simply real things. The expression on the girl's face is not, first and foremost, any part of a language of photography. It's body language. The artist might be using that somehow, but it begins as a real thing based on a language of its own.
Arrangements of light and shadow might be a better choice, since these, while real, are not generally any part of a language of their own. Here we run into the problem of whether any "language" in play is photographic, or part of a more general language of visual art.
There probably are language-like things in play in some photographs, which are specifically photographic. You could reference other photographs, there are lens effects one can use such as depth of field or more generally managing the plane of focus. See also P. H. Emerson. You can use lens flare. The use of monochrome is not exclusive to photography, but it certainly rare elsewhere. Other things, vignettes for instance, are tropes which could apply to any visual art, but appear almost exclusively in photographs.
Regardless, I think any attempt to pull apart the communicative aspects of a photograph into "photographic language" versus everything else is going to be pretty hard.
There are ways to try to express things you want to communicate, when making a picture. Some of them are about directing the model, others are as much about painting as about photographs, and some are purely photographic. I think it might not be the best use of our time to try to categorize them too much, but it's definitely worth our time to think about them.
The more we know and the more conscious we are of everything that goes into a picture, the better the chance we have, surely, of communicating what we want to say.