I think there is a lot said about jazz that can be distracting... there are traps to avoid and so on.
Firstly, quite often and quite widespread, there can be a feeling that there is Music and there is Jazz. This simply isn't true - it's all music, whether you label it Classical, Folk, Jazz whatever.
Feeling these different 'branches' is, to me, a way of thinking. And that comes with doing it, listening, playing, having a go - all in all gathering an understanding.
If you are used to playing "from the dots" you may find it difficult to make the jump to 'no music' - I did and still do. And I find that hearing harmonies, chords and chord changes is something new, too.
Well done on Grade 3, but a jazz exam, I think, needs time to work to - as Tsax said, listen lots and play lots. A lot of jazz is driven by the rhythm section, so listen to the drummer and bass player.
I am trying to say it is different, but not a million miles away, it's all music - it's all moving through musical experiences and it's great!