On the one hand: posture, alignment, breath support, vocal placement, resonance, tone, dynamics, and what have you. On the other: modes of the major scale, 2-5-1's, approach notes, alterations, substitutions, transcriptions, and many others.

Which one to focus on if you want to be a jazz singer? Singing teachers typically concentrate on vocal technique, paying little attention to the musicianship side. If you want to learn about jazz theory, you're often better off learning from an instrumentalist. Then again, instrumentalists typically don't know too much about singing. Another question is, which aspect should be practised to what extent, and how. The voice gets tired fairly easily, so it's vital to find an efficient way of learning. 30 minutes of technique and another 30 minutes of applied jazz theory? What about interpretation, or repertoire work?

I can't say that I know the answers to the above questions, nor do I believe that anybody knows them, for that matter. It is an individual thing. However, I am convinced that in order to be a jazz singer, one needs to have a degree of understanding of both vocal technique and jazz musicianship.