Those seemingly random notes are improvisation. Depending on the arrangement and/or preferences of the individual player, yes, those notes may be based on the c

Those seemingly random notes are improvisation. Depending on the arrangement and/or preferences of the individual player, yes, those notes may be based on the chord progressions... or based on a particular scale or mode ("modal jazz")... or pulled together from a catalog of memorized melodic fragments... or some combination of all of the above. In general, players who are also proficient composers tend to be the best improvisors. Players who are only players can be good improvisors, but their improvisations tend to be more on the mediocre / less inspiring side. Unfortunately, it sure seems to me that we've had less and less good jazz composition over the years, which might explain why more and more jazz improvisation sounds rather lousy. On the other hand, some improvisation made by expert jazz players really does sound very strange on purpose, e.g., the "Science Fiction" recordings of Ornette Coleman. You might like it, you might not, but either way, it's pretty far out there.