Hey, Ed, I was only kidding about holding the model's hands.
I sense now that you are quite serious about trying to understand this stuff. I'll try to do my best to make it clear.
"Vision" has nothing to do with subject matter. Not with landscapes, studio setups, portraits, etc. Others have said very clearly what "vision" is. To paraphrase their fine answers--it is what is behind your way of looking at the world. Your way of looking at the world would be your "style."
Now, style and vision are not something one ever tries to incorporate. They are things that, over time, emerge from the work you have done. Whereas a photographer's style can be articulated, discussed and analyzed, vision is less amenable to those things. There would readily be consensus about a photographer's style, but not, in all likelihood, about a photographer's vision.
Let's think of the work of two well-known portrait photographers, Richard Avedon and Arnold Newman. (This will be brief--let's not get bogged down in arguing about particulars of my comments--the general point is, of course, up for discussion.) Newman's style is to place figures in the context of their environments, his pictures are sharp and clear, there is a strong structure and sense of abstraction underlying each picture. Avedon's style is very different--from his mature style his figures are generally center seen centered against a white background. They are also sharp and clear. I don't think any knowledgeable viewer would ever mistake an Avedon for a Newman or vice versa.
Now what about their vision. I would say the Newman sees people as being at home in their worlds, which would reflect that he feels at home in the context of his surroundings. Avedon, on the other hand, sees people as being alienated, cut off from their surroundings. This would reflect an alienation he himself feels.
Others may have a different take on these last few sentences--my very brief and not comprehensive analysis of their vision (which may be right or wrong--please let's not get bogged down in particulars--it is a general point I am trying to make), is open to contradiction, interpretation, rebuttal, etc. it is not, nor could it ever be definitive--it is my opinion based on my understanding of human functioning, Again, it may be right or wrong.
So the difference between "vision" and "style" is clear, yes, Ed? Now how about "composition." Avedon composes so that his sitters are centered. That compositional device determines his style. Newman composes so that there are visual tensions carooming back and forth throughout the picture space (this is very general--there are lots of exceptions in individual pictures). These compositional strategies (though they are not intellectualized they can still be called strategies) determine the style, which in turn defines the vision.
Now, as I said above and this is a point too important not to repeat, especially for those who are trying to find their way: one does not choose either compositional strategies, style, or vision. They are things that emerge as a function of the working process. They are nothing that one tries to adopt. After one has been working for a number of years, you look back on what you have done and you see, readily or not, what all those things are. To intellectually choose one or to follow so-called compositional "rules," would be fine for a commercial photographer (I agree with you somewhat here RAB), but not for an artist or for an aspiring artist. These things come from who you are in the deepest sense. They choose you, You do not choose them.
If you choose them you would only be doing something more superficial than might otherwise emerge. You may get something clever and catchy--and you may make good pictures and get noticed (it happens all the time), but because they are from the mind rather than from the heart or soul, because they do not emerge as part of an ongoing organic process, it is likely that the resultant pictures made by choosing a style or a vision, will not last nor join the galaxy of great art that has persisted through the ages.
(Apologies for my earlier comment about "those who are ignorant." When I am the target of comments meant to disparage me, I do react. I did not mean to use such a broad brush. These discussions should be good natured, even if there is serious disagreement.)
Michael A. Smith