If the instrumentalist is really a genius, s/he is not competing with the vocalist for attention. A great "side man" works hard to complement the singer, not upstage him or her. There's no way you can look good by making your band mates look bad.

And yes, the musicians are often playing for other musicians, or at least very knowledgable aficionados. I sometimes take friends to hear jazz performers. As often as not, they miss the whole point of a great solo. If you can't grasp all the possibilities a chorus may afford, it's difficult to appreciate the choices the soloist actually makes.

      - Mark