I feel in some ways the answer is simpler than we think it is, because we could ask the same question of other types of artists. For instance, when do you call a dancer a dancer?
When they've studied the craft and are fully dedicated to the pursuit and performance of it. Fully understanding the techniques, positions, history, styles, etc...
The opposite it is also true: I can change the oil in my car, but obviously I wouldn't be called a mechanic.
The only other caveat would be the (true or false) opinion of the viewing audience when it comes to theater (dancer, actor, magician, you name it.)....Some people have perfected their act to a point where the audience is eager and easily ready to 'call' them a magician upon witnessing their performance, and yet they don't fully know that possibly the guy onstage has a very limited amount of knowledge beyond the scope of his own small act. The audience CAN BE FOOLED at times.
But if you're talking magician to magician, you should obviously know your history, the classics, the masters, the well known moves, themes, vernacular, etc... and have a definite goal in deciding what you are going to work on and present and hopefully make a living at it -- be it close-up, stage, mentalism, etc...
And like teachers, plumbers, dancers, etc....they all continue to learn and expand and grow on a continuing basis as the world grows, and as technology, new inventions and techniques continue to evolve.
In short, a 'true' magician respects and understands the art of performing magic as an artform.
Them's me thoughts. : )