@Orpheus - I appreciate your passion for jazz. What I don't get is why you think I am having trouble "accepting" anything?? I was merely trying to explain to you the kind of work it takes to become a professional musician of any kind - my comments were in no way specific to classical music, and I am sorry if this was not clear. I will let Frogman's great answer stand - he writes much more clearly than I, that's for sure.
@Charles1dad - yes, some classical musicians do still improvise, though this is largely becoming a lost art in the classical world. Even well into the 19th century, almost all musicians had to develop some ability for it, but after that point, the incredible technical advances in both instruments and players brought about such specialization that the focus now is almost entirely on learning to play the instruments as well as possible. It also has to do with the sheer size of the "standard rep." There is so much music out there that the orchestral musician must know now that most feel there is no time to develop improvisational skills that they would probably never be called upon to use. This is a very sad thing, IMO.
That said, there are still many who do on a regular basis, though in a different way from the jazz musicians. They are mainly keyboardists - those who perform baroque music are the best example. A harpsichordist must do what is called "realizing" the figured bass. Basically, the composer has written down some figures (numbers) below the bass note that tells the performer what chord is required. It is entirely up to the performer how this chord is spaced, or voiced, and sometimes even the chord required is flexible. None of the rest of the part is written out, just a bass note and these "figures." So the harpsichordist is making up his entire part above the bass note, often elaborating it. Singers and instrumental soloists also often improvise ornamentation of their melodies in baroque music, as well, and there are many musicians very adept at this - much of the time, it is done on the spot, not written out beforehand. There are also still some soloists who improvise cadenzas on the spot in their concertos, but this is becoming more rare. Stephen Hough is one example. In undergrad, besides my horn performance major I also did a music theory major, and had to take a course in keyboard harmony, including learning to 'realize" figured bass. It was fun, though I have not done it since, and would have to brush up on it to try it - that's not something I could just sit down and do anymore.
This is not so different from what jazz musicians do as you might think. Once you know more about how jazz works, musically, much of the mystery goes away. To grossly simplify it, (and Frogman, feel free to jump in and help me out here) let's say you have a group getting together in a club to play a couple or three sets of standards, a typical one night club gig. Yes, they are improvising, but within a strict framework. There are standard harmonizations and forms for all of the standard tunes, which these players all know (a significant part of their study and practicing). If they haven't played a tune before that is going to be played that night, they also have resort to what are called "Fake Books," which list songs and their standard harmonizations, etc. This is how people who haven't played together before can still get together and sound as if they have - they can study up beforehand, and also talk through stuff beforehand and even on the spot if necessary. So they are actually working within a strict system, though it does not appear that way. This is why even a group that has played together a very long time and that takes requests sometimes has to refuse one, if they don't all know the obscure tune requested and don't have time to figure it out because of lack of a "book" on hand. I've witnessed that happen before in jazz clubs (and I will admit to have mischievously thrown out an obscure tune at my friends, in fun), though usually experienced players will have an almost encyclopedic knowledge of the tunes. Some groups that have been playing together for a very long time would be very hard to "stump" that way. Hope that somewhat answers your question, though Frogman could give a much better description, I'm sure.
