The word photograph is no longer useful as the generic term in photography. With the rise of digital photography, the file that is displayed on your computer screen is no different than a drawing or a .pdf. I try to use the term image for the raw data file. You push a button, and an image is stored on the chip. Later, the image is transfered to your computer, for editing and/or printing.
Many terms from chemical photography are still in use, and still apply to digital photography. Here are three aspects of an image, allowing the viewer to apply criteria as warranted.
By far the most number of images are snapshots. A snapshot is a recording of an event and the people at the event. The technical quality and artistic composition are rarely a major consideration. You want to know who was at the party. You want to see Uncle Morty back when he had hair. You want to remember the people around you at your birthday. You want to remind yourself of your vacation.
Snapshots don't have to be good pictures or good photographs, but it helps.
A picture tells a story. Within a single image, the viewer understands what is going on. The story can be an action, a mood, a time, a location or any combination. What makes a good picture is largely subjective, much like any art form, and not all pictures work for everyone. However, most good pictures are widely recognized as being great shots. The technical aspects of the image are secondary to the moment being captured.
Pictures don't have to be good snapshots or good photographs, but it helps.
A photograph is judged on objective criteria: Lighting, clarity, composition, etc. You don't have to be a camera geek or a Photoshop expert to produce a really fine photograph, but the skillset necessary to produce consistently great work is more than just an expensive camera. Some great photographs are pretty to look at but boring outside of their didactic milieu.
Photographs don't have to be good snapshots or good pictures, but it helps.
Most images are a combination of snapshot, picture and photograph. You can compliment a good picture of a friend without implying anything about the snapshot or photograph aspects.
Nonetheless, the distinctions have value. It is better to have a grainy and static snapshot of your grandmother than none at all. It is better to have a really interesting picture that stays with you even if you don't know anyone in the shot and the lighting isn't so hot. It is better to have an accurately detailed photograph that's worth looking at even if you don't care about the subject matter and it doesn't do much but look pretty.