For the question in the title: I came from the technical side of the craft, so I'll break the mold this time...
Since the advent of automatic exposure control in electronic cameras
(0): the point
I would consider someone being graduated from the novice state, is
when he finally managed to consistently produce usable shots with Manual mode.
Because every adjustments that entail in
Manual mode: sensitivity, white balance, aperture, exposure time, and focus distance, are the fundamentals variables in all camera-based optical imaging works. Ability of making these variables work together or compensate each other to produce usable snapshots is a mark of someone who understands the basic mechanism behind his craft. Once accomplished this, he could proudly peel off the "novice" or "beginner" label he had given to himself.
A use of Manual mode also usually involve reading the camera's full user manual (1), which helps in the "know thy camera" department as well. It baffles me that many people in general either don't RTFM on their gadget, or mistook quick start guide as the manual; then proceed to ask around about things that manufacturers had already spent effort documenting up front...
Even with that said though, this doesn't mean that an intermediate-level or expert photographers couldn't or shouldn't use
Auto or similar modes when appropriate or sufficient. The rite of passage in
Manual mode however, makes sure that he knows which exact intervention was needed in scenarios where the camera's automatic adjustments fail to give desirable result.
(2) Bonus points when he also knows how to do so in the least-effort fashion; including by using semi-automatic
whatever-priority modes or scene-position presets that the camera provides.
For the matters beyond the camera operations: like having eyes for spotting good scenes, creative uses of impromptu scene compositions, creating and managing artificial scenes and lighting, making optimal/creative uses of found lighting, achieving fast lens-open-to-shutter-press, ability to capture
both details and hints of movement in fast-moving objects as a still, and ability to creatively position optical quirks or custom exposure time as photographic effects, etc... I'd consider those
rather are matters that distinguish between intermediates and experts in each photographic
sub-fields.
(0) For the film age before the automatic cameras, I would rather draw the line at someone's ability to consistently produce usable shot at all.
(1) Not the quick-start pamphlet or abridged booklet that's often provided in the camera's box! I meant the full version that is a few-hundred-pages PDF file provided in the CD or made available on the manufacturer's website.
You don't have to read it back-to-back to be effective; just jump directly to the section that concerns usage relevant to your current photographic subject/practice session. Eventually, your curiousity would get better of you; and you would find yourself casually sift through the nearby chapters on your own.
The manual would also narrate on how you should take care of your camera (including quirks and unexpected catches you might need to watch out for), which I think can be important too; DSLRs and mirrorlesses are not cheap. Some would even teach you how to hold the camera in the way that manufacturer thought to make an "optimal" shooting experience on that camera model; which can be interesting to read and compare with the way you are currently using.
(2) Or clear, normally-desirable result; but without the aesthetics/artistic quality the photographer was looking for.
