I tell my clients to demand a correction and request a retraction. The reason is, demanding a correction is not only necessary in certain circumstances to seek general and exemplary damages, but also because corrections are much easier to obtain.
Retractions are much more difficult to come by, however. Think about it.
A correction is an adjustment or substitution for something that is wrong. It allows the publisher to retain certain aspects of the story or alleged defamatory statement or statements. The main idea may be preserved.
But a retraction is a total withdrawal, and it is often very difficult (but not impossible depending on the facts) to negotiate a retraction once litigation has commenced because it means the defendant loses face.
But it never hurts to ask . . .