There is no single word for an informal story, several formats can be used in both formal and informal ways.
Types of stories that could be informal include; folk tales, anecdotes, fables, Fairy Tales, nursey rhymes, myths, yarns (long, rambling stories) and fables.
An informal story will appear more casual, and will not be restricted by formal structure or convention. An informal story may be more suited to spoken language than written (such as many folk tales), and may include idioms and sayings.
A diary or journal is an informal record of a person's experience.
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writting of informal letter
An autobiography
It's called the plot.
The problem in any story is known as the conflict.
an informal letter to grandfather describing the experience in a mall