There are 3 game style modes: Action, RPG and Story.
Action makes all dialogue choices automatically, predetermined by Bioware. Combat is manual, similar to the previous games.
RPG is business as usual, allowing you manual dialogue choices and normal combat experience.
Story is manual dialogue choices, with minimal combat. Story mode is locked to the Narritive Difficulty.
The actual adjustable difficulties are similar to previous games:
Narrative This difficulty level is intended for players who are more interested in story than combat. Shepard and squadmates are
stronger, weapons are easier to handle, and enemies are weaker and
less aggressive. This is a nonrepresentative Mass Effect 3 combat
Casual This difficulty is intended for players inexperienced with shooters. Shepard is stronger and does more damage, weapons are easier
to handle, and enemies are slightly weaker and less aggressive.
Normal This difficulty is intended for players with experience playing shooters and RPGs. This is the baseline Mass Effect 3 combat
Hardcore This difficulty level is intended for players looking for a challenge. Enemies are powerful and aggressive. Advanced gameplay
Insanity This difficulty level is intended for players seeking the ultimate challenge. Enemies are tenacious, react quickly, have heavily
upgraded weapons, and use their powers mercilessly.
To answer your question succinctly: Mode determines manual or auto dialogue and combat difficulty. The adjustable range modifies combat for RPG and Action modes. Story mode is locked to Narrative.