Speaking from a literary viewpoint, there are several main differences between a comedy, a tragedy, a romance and a history.
A comedy was first referred to in the medieval times as any writing which ended happily. There has since been added literature dealing with serious or dramatic themes, but doing so in a lighthearted manner. Then there is the dark comedy which deals with the macabre, in an unsettling satirical manner.
A romance, during medieval times, dealt with often historical or heroic deeds. It did so in the form of allegorical poetry, so as to romanticize the events. It is commonly a rendering of light and amusing characters that concludes with a happy ending.
A tragedy deals with tragic events and usually result in the ruination of the main character.
A history is a factual account of events. It involves the chronological relating of facts about real people and situations in a straightforward manner.