“Okay, but what is Improv really?”

In terms of creativity, it’s more useful to describe what it isn’t.

Consider a jazz saxophonist soloing over Giant Steps.

The architecture of the song is AABA. You don’t want to change that. You want it to stay the same. So that’s not where the improv lives.

The design of the playing (tone, timbre, instrument technique) is unique to the player. You don’t want to, on some notes sound like John Coltrane and on others sound like Charlie Parker. You want to maintain your sound. So the improv doesn’t live there.

What does change are the notes.

So every time you play Giant Steps, the architecture stays the same: that’s the song.

Your “sound” stays the same: that’s your style.

But the notes change. And that’s the improv.