A composition is a map that traces a past journey.
An improvisation is a new journey.

One could also say that a composition contains the highlights of a past journey.
Like a set of photographs: selected moments from a certain period.

An improvisation is a journey and while it contains highlights, it may also contain those moments of the journey that are not glimpsed in the set of photographic moments: waiting for the train to arrive, lying in bed and staring at the ceiling, walking to the corner to see a new vista…