Fine art is notoriously difficult to describe, once you get beyond "I know it when I see it". But I think you're on to something with the notion that your art is not something anybody else could grind out in a few minutes using widely available tools.
People smarter than me have pointed out the two components to a piece of art. First is the artist's eye, or concept, or vision, whatever you want to call it. Second is the craft element, the attention to detail in execution. You really need both for something to be considered a work of art. Hence there are lots of nicely crafted images of sunrise under Mesa Arch out there, shamelessly pirating David Muench's original vision without adding anything new. There are also countless images with some potential that fall down on the craftsmanship side.
So trying not to be trite, a fine art photographic print is one that starts with a potential image you see that no one else has noticed. You then apply every skill you have learned to express that unique vision, saying what you mean to say, crafting the very best print (as a unique physical object) that you know how to make. I like David Plowden's response to a custom printer who boasted of being able to make a better print from one of Plowden's negatives than Plowden could make himself. To paraphrase, he said, "You may be a better printer, but you don't know how to print my photograph the way I want it to look".
When it comes to the print as an object, inkjet prints are a bit different from traditional darkroom output, where each print is another unique effort, even if you're trying to repeat a choreographed dodging & burning plan. Once all the hard work of image editing and optimization is done, reproducibility is much more direct. Brooks Jensen of Lenswork has given this area a lot of thought, and some of his observations about the nature of art when craft becomes more repeatable are very provocative. But even if I can print an edition of one or of 100, it's still my print!
Finally, it's not just marketing to let potential buyers know what went into a specific print. The image of course must stand on its own two feet to attract interest in the first place. After that, it's appropriate to inform someone that you (for example) personally printed the image using an archival pigment inkset on 100% cotton rag paper, matted with conservation mat board and custom framed. An accurate C.O.A (certificate of authenticity) does add some value to the image.
Just my 2 cents.