Watch out for literary critics. They can get feisty.
Though lit crit peeps use the term "narrative theory" like it ain't no thang, not everyone has approached narratives in the same way. Some narratologists have taken on a cognitive approach that explores links between narrative structure and the mind. This includes the role that narratives play in making sense of both our own and other people's actions—as well as the world in which we live.
Other theorists have taken a rhetorical angle. For them, narrative is an act of communication—its purpose is to tell a person (or group of people) something. While this approach may explore the individual parts of a narrative, it's more interested in the bigger picture. These kinds of critics are into thinking about how texts are created to affect readers in certain ways, (whether the author is conscious of this or not.
Some other narratologists get their nerd on by studying forms of narrative they feel have been given raw deal. Feminist theorists, for example, have pointed out that narrative theory has often focused on a single kind of narrative—basically, the kind studied by Propp and Todorov. That's led to the idea that this particular form of the narrative is the only form that narrative can take, and so it gets all the glory.
Feminists, on the other hand, argue that women may write different types of narratives—narratives that we should take seriously rather than ignore or run down. Feminist theorists also think that structuralism in general can be way too narrow in its focus on the text alone; these theorists say that we need to think about historical and social factors too.
Women's writing isn't the only area that some people feel has been left out in the cold: academics working with children's literature have made similar complaints, and the same goes for "unnatural" narratives. By "unnatural," we're talking about experimental texts that don't follow the usual template and mess around with time and space.
This isn't a new thing, and it doesn't just apply to "artsy" texts like Lewis Carroll's Alice stories and Jonathan Swift's satires, which have intentionally screwy narrative structures. Even when a narrative seems to be realistic, there's no reason why it can't become unrealistic at certain points—in fact, this can be a pretty effective device. Theorists have therefore been annoyed that, despite all this, narratology has often been all about realism.
In addition to these debates, theorists have sometimes had different ideas when it comes to definitions. We've already seen that Genette and Stanzel put together two of the most detailed models of narrative theory, with Stanzel using familiar terms such as "first-person" but Genette, however preferring "voice" to "person" for a couple of reasons. First, he sees "person" as having a psychological vibe that he's trying to stay away from— he's a structuralist, remember?
Second, Genette believes that "voice" can include what we'd usually call "person" but isn't limited to it: he's looking for a broader term, and "voice" fits the bill. We're not saying that these guys are at loggerheads; it's just that theorists have their own ideas about how to sum up these different types of narration.