An action story is similar to adventure, and the protagonist usually takes a risky turn, which leads to desperate situations (including explosions, fight scenes, daring escapes, etc.).
An adventure story is about a protagonist who journeys to epic or distant places to accomplish something. It can have many other genre elements included within it, because it is a very open genre.
Within film, television and radio (but not theatre), drama is a genre of narrative fiction (or semi-fiction) intended to be more serious than humorous in tone, focusing on in-depth development of realistic characters who must deal with realistic emotional struggles.
A Thriller is a story that is usually a mix of fear and excitement. It has traits from the suspense genre and often from the action, adventure or mystery genres, but the level of terror makes it borderline horror fiction at times as well.