The humorous story is told gravely; the teller does his best to conceal the fact that he even dimly suspects that there is anything funny about it; but the teller of the comic story tells you beforehand that it is one of the funniest things he has ever heard, then tells it with eager delight, and is the first person to laugh when he gets through. (Later Twain says that it is "a pathetic thing to see.")

-Mark Twain a.k.a. Samuel Clemens (1835-1910) in How to Tell a Story

Twain was describing the verbal telling of the story, but what is the distinction between the humorous and the comic story if they are told in writing rather than in speech? Is there a distinction? Or can one write the humorous story gravely and chuckle in the written comic story?