Narrative art is art which represents elements of a story.
Genre and history painting are types of narrative painting.
Genre paintings depict events of an everyday sort,
like Jan Steen's "The Marriage"does,

whilst history paintings depict famous events,
like "The Raft of Medusa" by Theodore Gericault does.
In my opinion, though, present day art world is not constrained to these two types of narrative painting anymore.

Michael Hussar "Gummer"

Aung Kyaw Htet "Red afternoon"

Norman Rockwell "Gossips"

Keith West "Salome with the head of the Baptist"

Cecily Brown "Teenage Wildlife"