Difference between “improvisation” and “extempore” [closed]

What is the difference between improvisation¹ and extempore² and where should one use each of these terms?

Solution 1:

Extemporaneously means, strictly speaking “without time to prepare”, though it has also acquired a secondary meaning of “without a prepared text or notes”.¹

Improvisation means an act of improvising. To improvise is to “act without foresight”, that is, without seeing in advance what one will do.²

These words are not always synonymous. Imagine a European classical musician asked to perform a set piece without warning. This musician will perform extemporaneously but without improvising. Now imagine a jazz musician asked to perform without warning. This musician will perform extemporaneously and also improvise the music itself.