A Genre is a definition of the story's focus and basic writing style.
A General story has elements of most genres, usually Suspense, Comedy, Action/Adventure and Romance, Drama or Angst (rarely more than one of those three).
Action/Adventure stories usually revolve around fighting other characters during a journey or quest. However, it can also be solely one or the other as both genres are usually given as one.
A suspenseful story is a story that focuses on the events leading up to an even greater one, which usually occurs as the climax, or after the ending. i.e. Studying for a test, Training for a race, fighting towards a greater evil...
A comedy is a story that focuses on humor and makes the reader laugh.
Drama is similar to angst. However, drama often deals with romance and conflict.
Romance is a story where two or more characters are in love. Usually two or three pairs will come together in love at the end, or are together and tested.
An angstful story is a story that often boarders on Romance where one character is in great emotional pain over a non-romantic problem such as abuse or similar.
Horror stories usually follow characters being terrorized by a killer or creature or some kind of problem which causes the reader anxiety, fear, and ultimately thrills.
Friendship stories bring two characters together as friends or focus on their friendship.
Stories with the genre of tragedy have multiple characters (usually the main characters) die. A great example of this is some of Shakespeare's plays like Romeo and Juliet, Macbeth, and Hamlet.
Sci-Fi usually deals fictional species causing danger or problems to human society, take place in the distant future, or involve space or time travel.
Like the title says, Historical stories deal with real historical moments, such as wars (ex. Civil War) or other big moments in time (ex. death of a political figure).
Fantasy usually deals with magic and mystical creatures of some sort.
Crossovers find characters from different stories, series or films coming together.
Prequels are usually set before the events of the series.
Remakes are stories that attempt to remake episodes.