A pro? Prostitute, of course! Someone who reduces themselves to a cog in the wheel of commerce, from wedding photography through Fashion/Still Life/ Food to reportage, dependant financially on an income from clients/ employers. A Hack, -thats the usual definition, but I have another.
I was once for a while, in the above category: it is difficult demanding and destroys most people completely in the end, or earlier, if they have a VOCATION.
A Vocation, or calling, as to be a priest, a nun, a doctor etcetera. So Ed Weston, Ansel Adams, Paul Strand , Eugene Smith and a number of the best reportage photographers. Like me they do their thing as it has become their thing. They are that. I AM a photographer: it is intrinsic to my being, to my integrity as a human: it is what makes me human, and like those guys I cannot imagine being otherwise at all. I did not do it to get paid for doing it. I profess photography: I am a Professional!! (But do not earn a penny from this now very expensive part of myself.
Does this help?
Ansel Adams once talked about this. His term for what you describe as a pro was a commercial photographer - which fits fine in your cog of the wheel of commerce analogy.
Take the late and great jazz musician Miles Davis. He did it his way. He loved his music and it was his life. If you want to come see him play - fine with him. If not - fine with him. Davis honed his music and expanded jazz. His work was cutting edge. Now compare Davis to the knock off bands that play in hotel bars or the piano player that plays in the local piano bar. They are there not for the musical ability but because the bar will sell more booze with live entertainment. They would I think be better called commercial musicians.
But in the end - Ansel Adams, was a professional. He made his living through photography. He had patrons that financed - especially his early work - him so he could develop his style. Adams nor any you mentioned above were commercial photographers but they were professionals, they taught workshops, they gave clinics and lectures, they made prints for galleries and they also make prints for individual customers. But like Davis - if you liked an Adams print and wanted to buy it fine with him and if you didn't fine with him.
So maybe we should use the Adams definitions. I think what many people refer to as professional photographer are really commercial photographers.
I've always thought of a commercial photographer as one who handles work that is specifically needed for a commercial purpose through specific requests by clients - product shots, copy art, head shots for talent, etc. He could be an artist, or he could create very artistic work. But that need not be the case.
And would we deny a given wedding photographer the title of "Professional" because his work isn't very artistic or cutting edge? He's not blazing new ground, his work isn't commercial because it's not for a commercial purpose, but why wouldn't we call him professional?
I wouldn't call jazz musicians who play in night clubs purely "commercial", I would call them working musicians and in most cases, they are also professional musicians. I'm not sure how they could be anything but professionals if they're required to carry union cards. They may be very good or just mediocre. Plenty of rock musicians are musically mediocre at what they do and yet plenty of them blaze new territory and advance the field. So what do we call them? Musically deficient commercial artists? I'm not so sure.
As for Ansel and Miles vs. the rest, you're seeming to weave into the definition some element of the quality of the work and/or the way they pushed the field and added to it. I don't think that's a dividing line we should use to call someone professional. It's a dividing line we might use to call them true artists or innovators, but it's not an element that has to exist alongside the definition of the term "professional". It may exist, but it need not.
This leads me to a distinction that comes to mind - I don't think a photographer needs to "make a living" to be called professional. Otherwise, we get stuck in the endless circle of "how much of his living?". Is it 50% or more? And we probably wouldn't want to say that it's merely making money at photography that defines "professional" because plenty of us make a little money by selling a photo here and there.
Perhaps the definition needs to include something along the lines of "is commissioned to perform photography and recognized by the community as a professional."
We are digging down deeper into semantics and given we have several different first languages represented here it is probably a hopeless effort ;-). However, in the interview with Adams where he made the distinction he did not imply or mean to imply that commercial photographers were not professional. In fact he said that he does commercial work from time to time and it benefits every photographer to do so.
It was that they worked on a fee for service (in the case of wedding) basis. Now many photographers such as those in the 40's and 50's that either worked for Life or worked for the NY Times, etc. were top notch photographers but they were doing commercial work providing images based on assignment and a few for service arrangement. A CNN photographer embedding with Marines in Iraq would be a professional photographer but his work is commercial.
A musician that plays for the Boston philharmonic is am employee who is on contract to provide a service but they have to be very good professional musicians. Where as Miles Davis worked for no one but himself.
To me it gets down to the following analogy. Most states have a license of professional engineer. You have to have an engineering or science degree from an accredited university and pass and exam. Once you do so you are licensed to do work in the public trust, survey, sign engineering design plans for a permit, etc. However, the engineers that designed the space shuttle or the new F35 fighter bomber required no such license. There is a parallel in the medical industry where some of the worlds best MD at Johns Hopkins Hospital cannot practice medicine off the grounds of Hopkins property because they are not board certified in Maryland or the other stats that have Hopkins Medicine properties.
They practice under the board certification of Hopkins when they are on site. Are these MD's any less a professional?
Photographers, musicians, artist, come in all shapes and forms. Some work for someone else. Some work for themselves but their output is fee for service and they go from job to job. Some are free lance - they do what they wish and then if someone likes it they buy it or they get grants to pursue projects. Some are on the staff of art schools and universities where part of they requirement is to impart their knowledge, skill and craft to the students and part is independent work - often funded under grants. Some are just freelance - making it on their own through the creativity of their work.
We all I think have a bias of what we would call a professional but I think when photography is a large part of a person's life and in some form all or a significant part of their income from photography or they make contributions to the art and/or science of the craft - then they are a professional.
They may be a commercial photographer - strictly working on fee for service, a academic photographer, a photojournalist or a free lance photographer - but they are still professionals. Now was Andy Warhol a professional photographer. Of course he was although he did a lot of other things.