Is it improvisation? Certainly not, because improvisation isn't new. Aside from folk music worldwide, most of the pipe organ performances in church service were improvised by the organist back in Early Music era. Their improvisation was similar to what we do in jazz improvisation. There is a chord progression, whether preplanned or improvised, then improvised melodies on top of it.
The most important thing in jazz music that sets apart from other kind of music is its groove. While other type of groove oriented music asks for tightness, jazz music calls for time feel against each other.
On top of the beat
On the beat
Behind the beat
For example, Erroll Garner's left hand is on the beat, while his right hand is always behind the beat, and that grooves. Drummer like Philly Joe Jones plays extremely laid-back ride cymbal while playing hi-hat on top of the beat. Then you bring monster bass players to it. Ray Brown, Ron Carter, they are all on top of the beat, way ahead of drummer, that drives the band. This is the thrills in jazz time feel, that makes jazz so unique.
Unfortunately it is often misunderstood if improvising is the most important thing in jazz music. It is only the second important thing. Still we want to play cool improvisation. Unless you are a genius, knowledge becomes important.