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closed as general reference by Jasper Loy, Barrie England, Andrew Leach♦, FumbleFingers, tchrist Jan 1 '13 at 21:09
This question is too basic; it can be definitively and permanently answered by a single link to a standard internet reference source designed specifically to find that type of information.If this question can be reworded to fit the rules in the help center, please edit the question.
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.