Dialogues, monologues, and interior monologues would be defined as narrative modes. These types of narration are rather definitively momentary, which means they might characterize a piece of writing but will not constitute an entire piece of writing.
We might also refer to dialogue, monologue and interior monologue as narrative methods:
The narrative mode is the set of methods the author of a literary, theatrical, cinematic, or musical story uses to convey the plot to the audience.
These moments of dialogue, monologue and interior monologue can be discussed in various ways but, importantly, do not need to be discussed in reference to any conventions or standards outside of the text itself. When considering genre, conventions and inter-textual considerations are of central importance.
Genres are formed by conventions that change over time as new genres are invented and the use of old ones are discontinued.
The term genre is reserved comprehensive description of an entire piece of literature. Though genre boundaries can be flexible or porous, we apply the term to describe the type of writing and methods applied across entire works.
Genre, then, is a concept of relationship between and across entire works of literature, whereas narrative modes can be discussed as individual moments within a text.