I despise the notion of "levels of photographer" but I am going to sketch out a sort of a progression anyways. Sorry about that, I hate myself a little right now.
The neophyte with the camera mainly sees the subject. The flower, Aunt Martha, the thing they want to take a picture of. Many camera-carriers happily remain here. These people famously photograph people with trees "growing out of their heads."
After a while, many of the more serious camera owners will read things that tell them about, well, various graphical features. They might notice leading lines, or intersections of lines. The might notice bright spots, shadows, the way the light falls. Most of the rest of the camera carrying community stop right here, slowly stirring around the short list of technical/graphical features they notice and photograph. These folks almost never photograph a person with a head-tree.
Serious photographers who are successful at communicating things, I feel, manage to simultaneously "go beyond" a sack of graphical tricks, and at the same time to return to the naive subject. Of course, I count myself among this sainted number. And, naturally, you as well, gentle reader.
The same applies to looking at photographs. The naive viewer says "what a pretty flower," the more sophisticated camera owner says "tsk, the flower is centered rather than placed on a Rule of Thirds Power Point," and the artist says "what a pretty flower" but in a more thoughtful way.
I think, I like to think because it's the way I do it, that the Serious Artist sees the whole frame of the photograph. They grasp the whole as a collection of forms and tones and lines and colors all in balance, or not, etcetera. And they they see a pretty flower, and the way the picture reveals the pretty flower without clutter (or with clutter, as is fit and meet.) But at the end of the day, it's still the pretty flower.