I think that the difference between these two concepts depends on the theoretical frame you adopt in order to deal with "narrativity". For instance, in Greimas' narrative semiotics, "life story" is specific narrative genre (there are many other genres: novels, legends, sagas, myths, etc.).
Narrative genres are composed of "narrative" units and relations: topics; roles, sequences, narrative paths, and so on. In this sense - at least with respect to the narrative theory of Greimas - the "narrative identity" of an actor, for instance refers to the topics and roles that caractérises the actor (in a corpus of texts, for instance) as well as the sequences in which the actor appears, the narrative paths which are typical for this actor, etc.
For instance, in brand communication, one might be interested to understand the topics, roles, properties, etc.that caracterize two competiting brands in a corpus of ads).
Narrative identity is a conception of identity, as something that includes differences, thanks to time. Life story is a methodological concept, which help us to understand narrative identity. Maybe this paper can illustrate the difference: https://www.researchgate.net/publication/232970568_Breaking_away_to_find_a_way_poverty_and_school_failure_in_a_Spanish_adolescent_life-history
Article Breaking away to find a way: Poverty and school failure in a...
Of course, "life story" can refer simply to any personal narrative - but you mean the Life Story approach to personality, correct? In that case, there are just two answers to your question I can think of offhand:
1. It may depend on whose specific narrative theory you are working with. Nuclear episode or self-defining memory? Autobiographical project or situated performance? They may differ subtly, but are basically the same: like social desirability and impression management, or cognitive dissonance and rationalization.
2. Within McAdams' Life Story theory of Identity, the life story is the narrative itself: the crucial memories that have been revisited and reshaped. Narrative Identity is the core "story of the self." It may incorporate the various rules or common themes that run through the multiplicity of stories.
I think of the term "narrative identity" as McAdams's theoretical model that includes constructs such as characters, generativity script, thematic lines, etc. The life story is the relationship among these elements at any point in biographical time.
I recommend you to look at the article by Habermas & Bluck (2000): Getting a life: The emergence of the life story in Adolescence. Psychological Bulletin, 126(5), 748-769.
Hi Emilia, Narrative identity are the stories we tell ourselves about ourselves - many short stories over time. The emergence of life story (McAdams) suggests these narratives form a coherence in late adolescence, thus forming the life story. Feel free to read my paper.
Life story is a way of coherently organizing in the here and now the many (at times contradictory) roles and values that we've held through time. In that sense, it is a narrative that help us create a sense of identity.