We discuss this a lot. I posted the following in another post:
"
Snapshot - image taken because the opportunity presented itself.
Photograph - image constructed to showcase the subject, remove distracting elements (foreground, background) lighting chosen to emphasize the key aspects of the subject... As Keith said, there's prep work involved. And the technical stuff (focus placement, right amount of DOF, appropriate exposure for the subject, right focal length) is there to place the viewer's focus where it needs to be. "
Even if you think about composition, etc. a good image is constructed. Take, for instance, even the presence of ambient light. We all know that the "quality" of the light greatly affects the end result. It is not uncommon for a photographer to come back to a specific location many times to get that special moment of appropriate light.
Good photographs distill the essence, and eliminate the superfluous. A good snapshot may capture much that is interesting, but on review, will show distracting elments, technical issues, etc. If you then go back and re-shoot, making specific adjustments to eliminate the negatives, and selecting those elements which contribute, you've moved the image-making from snapshot to photographs.
Snapshots often rely on the context for their meaning: it's YOUR kid, or someone YOU know, or someplace YOU really like. Take away the "YOU" and the viewer is left with... what? What clues have you as a photograher left in the image for a viewer to be able to relate to that image? That's the problem for most snapshots - they rely on the viewers knowing WHO the subject is, WHERE it is, and WHY the image was taken. And if you show the image to someone who has no such connection - what do they then grab onto?