'Specialist' is one of those unfortunate weasel words that can mean different things in different contexts and at at different times.
My mind is drawn to this question by a thread of Comments on Conductive World's Facebook page in which this word comes to the centre of attention:
Mária Hári spoke in English, in England, in 1970, about the essentially psychological/pedagogical nature of the work of conductors. Some of this has now been posted on line by Susie Mallett. I agree with Susie's view, the passage that she quotes is one of the best things that Mária wrote and well worth further airing. Read it for yourself on Susie's Conductor blog. When Maria was good, she was very very good:
What has attracted Facebook discussion today has been Mária's concluding point, that conductors' work did not proceed in isolation. She was referring of course to 1970 and András Pető's little institute just three years after he had died –
...there are specialists in every profession who are helping regularly.
All these years later, and looking round the world, some conductors clearly do work in such a context, variously arranged according to where they are, some most certainly do not, and most conductors presumably fall somewhere in between. How their practice measures up within Mária's central theme in the passage quoted from above, I have no way of guessing. Again along some sort of range, I would guess.
I do not know the precise meaning of the word 'specialist ' referred to here from her work in Hungary in 1970. Indeed I do not now know what it meant to me in England in those distant days. Had I been at that meeting I suppose that I should have heard it as meaning medical specialists, though I might have been wrong.
In today's English, British English anyway, the word 'specialist has no single, simple meaning. The situation is confused in English education by use of the word 'specialist' to denote both a defined administrative category of school and occasionally and informally as a bit of a euphemism for 'special'. So a 'specialist school' in the English state sector may provide either a particular specialist curriculum, or be a coy way of referring to a special school for disabled pupils. At a formal level, of course, it is altogether appropriate to refer to a 'specialist special' school'. And there are indeed such schools.
In British medicine. I think, a specialist is a consultant. I could be wrong.
I like to think that foreigners organise their use of language rather better than we do in this country, but I could be wrong there too.