Narratology is a branch of structuralism but it has achieved a certain independence from its parent. Narratology is not the reading and interpretation of individual stories, but the attempt to study the nature of 'story' itself, as a concept and as a cultural practice.
What narratologists do
1) They look at individual narratives seeking out the recurrent structures which are found within all narratives.
2) They switch much of their critical attention away from the mere 'content' of the tale, often focusing instead on the teller and the telling.
3) They take categories derived mainly from the analysis of short narratives and expand and refine them so that they are able to account for the complexities of novel-length narratives.
4) They counteract the tendency of conventional criticism to foreground character and motive by foregrounding instead action and structure.
5) They derive much of their reading pleasure and interest from the affinities between all narratives, rather than from the uniqueness and originality of a small number of highly-regarded examples.