CyberGene For instance, sometimes there are classical pianists who play jazz transcriptions (from actual performances of Bill Evans, Chick Corea, Keith Jarrett, etc. and even I have recorded one such on my YouTube) and when you compare it to the original there's always this lack of feel. They tend to apply classical (Romantic) feel to a jazz improvisation and that messes up with the rhythm and drive.
Have you heard Wang’s “transcription” of Art Tatum? It is exactly what you’ve described above!
The first thing “classical musicians” need to get through their thick heads is that Jazz improvisation is not “making it up as you go,” but rather structured improvisation based on a common theme; which, believe it or not, has a beginning, a middle and an end; even if not in the overly dramatic sense reminiscent of “The Romantics.”
Also, playing from someone else’s transcription is not a bad thing for “practice,” but the only way to truly speak this ‘idiom’ well is by getting down on your hands and knees, and transcribing the material yourself; it’s as close as you can get to the mental process involved within this or that jazz pianist whilst in active ‘improvisation’.
Of course, the first thing is to study “jazz harmony;” which is no more than conventional harmony evolved, so that when you hear an F# and a B (natural) within the context of a C7 you will know that these are not “wrong notes,” but rather very right for/within the jazz idiom. This concept is primarily based on “borrowing” from other chords and even from other keys without necessarily modulating, and it allows “Jazzers” to stretch things to their limits; which leads to some interesting, non-diatonic, musically dissonant situations that would otherwise not fit; if analyzed from a more diatonic/classical perspective.
Of course, there’s more to it, and something like this could further illustrate what Jazz is all about:
Note: “Jazzers” is used ironically!