What is a ‘Continuation’?

In the most general sense, of course, everyone would understand the word ‘Continuation’. It implies, one would assume, an ‘unfinishedness’, or incompletion, in the initiating narrative: it may be that the ultimate fates of some of the protagonists are unknown, but intriguing; it may be that a narrative thread is left hanging; it may be that some objective set for the protagonists is unfulfilled; it may be that there are mysterious events which seem to want explanation. A ‘Continuation’, in other words, fulfils the audience's, or the reader's, expectations, and ensures that their curiosity is fully and perfectly satisfied. As Renate Blumenfeld-Kosinski says, pertinently, in relation to the Voeux du Paon cycle:

However obvious this seems, the trouble is this definition is not quite specific enough to deal with what it is conventional to call ‘a Continuation’, as it might also seem to refer to other narrative forms.