I enjoy the harmony talk, but you don't really need that to PLAY jazz, as much of it is about style of playing, intonation and rhythm... aka the "swing". A good way to learn a jazz tune is to dump all the extensions, play the chords in their basic form as you know them, learn the tune, and then add the extensions you like. At least when you are just comping.. some extension notes in the chords are there because they support or don't conflict with the melody in the tune..

Jazz is much about rhythm, feel and making up stuff out of the usual box.. (I don't advocate not learning the jazz lingua, though).. so, playing 7ths and 9ths doesn't in itself, make up a jazz tune..